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重庆市2015年(春)高三考前冲刺测试卷数学【理】word试题及答案

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI General Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce defens e and army modern, and rich "one countr y, two systems" pra ctice a nd advance country unified, a nd go peace devel opme nt road, and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" to conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an ar ti cle does not go int o a link, no leakage of conducting a compre hensive study, a nd combi ned with their own dutie s and responsibil it ies, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht learni ng XI on stri ct party of di sci pline a nd r ules di scuss es ex cer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal innovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Pha se ha s the a dvantage of time to focus on fast, to hig hlight the t heme, focuse d, result ; often lear n the adva ntages of flexible fi t, form, subtle, conti nue s to

2015 年(春)高三考前冲刺测试卷 数学(理工农医类)
一、选择题:本大题 10 小题,每小题 5 分,共 50 分.在每小题给出的四个备选项中, 只有一项是符合题目要求的.
(1)已知集合 A ? {x x ? 1 ? 0}, B ? {x x ? 3 ? 0} ,则 ?R A (A) x 1 ? x ? 3

B ?(



?

?

(B) x ? 1 ? x ? 3

?

?

(C) x x ? ?1

?

?



D



? x x ? 3?
(2)已知纯虚数 z 满足 (2 ? i) z ? 4 ? 2ai ,其中 i 为虚数单位,则实数 a 的值为( (A) ?4 (B) ?2 (C) 2 (D) 4 ) )

(3)已知函数 f ( x) ? ? (A) 0

? log 2 x, x ? 0 ,则 f (0) ? f ( 2) ? ( ? f ( x ? 1), x ? 0
(B)

1 2

(C)1

(D)

3 2


2 (4)已知命题 p : ?x ? R , x ? 2 x ? a ? 0 ;则“ a ? 1 ”是“ p 为假命题”的(

(A)充分非必要条件 (C)充要条件

(B)必要非充分条件 (D)既不充分也不必要条件

(5)以坐标原点 O 为顶点, x 轴的正半轴为始边,角 ? , ? , ? 的终边分别为 OA , OB , OC ,

1 OC 为 ?AOB 的角平分线,若 tan ? ? ,则 tan(? ? ? ) ? ( 3 1 1 (A) (B) 4 3 2 3 (C) (D) 3 4
(6)某几何体的三视图如题(7)图所示,则该几何体的表面积为 ( ) (A) 8 ? 2 2 (B) 8 ? 4 2 (C) 12 ? 2 2 (D) 12 ? 4 2



2 正视图 侧视图

2
俯视图

2
题(6)图

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng programmes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the eve ryday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For any unit or i ndivi dual, obj ectively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip betwee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, always kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on May to broke more of window glas s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't peo ple manageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live peo ple, time l ong ha s di dn't pe opl e tube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s" . Lear ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the key is i n use , do, li ne. I n parti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI Gener al Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce defens e and army modern, and rich "one countr y, two systems" pra ct ice a nd advance country unified, a nd go peace devel opme nt road, and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" to conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cle does not go int o a link, no leakage of conducting a compre hen sive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht l earni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal i nnovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t hem e, focuse d, result ; often lear n the adva ntages of flexible fi t, form, subtle, conti nue s to

3 ( 7 ) 已 知 函 数 f ( x ) ? ax ?

1 2 x 的 导 函 数 为 f ?( x ) , 且 f ( x) 在 x ? ?1 处 取 得 极 大 值 , 设 2

g ( x) ?

1 2014 ,执行如题(7)图的程序框图,若输出的结果大于 ,则判断框内可填入的 2015 f ?( x)
) (B) n ? 2015 (D) n ? 2015
2

条件是(

(A) n ? 2014 (C) n ? 2014

开始

(8)直线 l 过抛物线 C : y ? 4 x 的焦点,且与抛物线 C 交于 A 、 B 两 点,过点 A 、 B 分别向抛物线的准线作垂线,垂足分别为 P 、 Q ,

S ? 0, n ?1
否 是 输出 S 结束

则四边形 APQB 的面积的最小值为( (A) 6 (C) 8 2

) ( B) 8 (D) 10 2

S ? S ? g ( n)

n ? n ?1

题(7)图

(9)有大小形状完全相同的 4 个红球,2 个白球,放入如题(9)图所示的九个格子 中,每个格子至多放入 1 个小球,相邻格子(即有公共边的两个正方形)中放入 的小球不同色,则不同的方法共有( ) (A) 32 种 (B) 40 种 (C) 48 种 (D) 56 种 (10)设 H 、 P 是 ?ABC 所在平面上异于 A 、 B 、 C 的两点,用 a , b , c , h 分

题(9)图

? 别 表 示 向 量 PA , PB , PC , PH , 已 知 a b

c ? h

b? c

a ? h

? c, a

b h

AH ? 1 , BH ? 2 , BC ? 3 , 点 O 是 ?ABC 外接圆的圆心, 则 ?AOB ,?BOC ,?AOC
的面积之比为( (A) 1: 2 : 3 ) (B) 2 : 3 :1 (C) 1: 3 : 2 (D) 2 :1: 3

二、填空题:本大题共 6 小题,考生作答 5 小题,每小题 5 分,共 25 分.把答案填写在 答题卡相对应位置上.
(11)某人在 5 场投篮比赛中得分的茎叶图如题(11)如所示,若 5 场比赛的平均得分为 11 分,则 则 5 场比赛得分的方差为 . (12) 设公差不为零的等差数列 ?an ? 的前 n 项和为 Sn , 若 S1 、 则 S3 成等比数列, a2 、

a4 ? a1



(13)已知二次函数 f ( x) ? ax ? bx ? c(b ? a) ,若 ?x ? R , f ( x) ? 0 恒成立,则
2

a?b?c 的最 b?a

小值为



考生注意: (14) 、 (15) 、 (16)三题为选做题,请你从中人选两题作答,若三题全做,则 按前两题给分.
deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng programmes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For a ny unit or i ndivi dual, obj ectively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip be twee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, always kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on Ma y to broke more of window glas s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people m anageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e tube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lea r ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the k ey is i n use , do, li ne. I n parti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI General Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce def ens e and army modern, and rich "one countr y, two systems" pra ctice a nd advance country unified, a nd go peace devel opme nt road , and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" t o conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cl e does not go int o a link, no leakage of conducting a compre hensive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht learni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal innovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t heme, focuse d, result ; often lear n the adva ntages of flexible fi t, form , subtle, conti nue s to

(14)如图(14)图, AB 为圆 O 的直径, O 为圆心, PB 与圆 O 相切于点 B , PO 交圆 O 于点 D ,

AD 的延长线交 PB 于点 C ,若 AB ? 2 , PB ? 2 2 ,则
. (15)以坐标原点为极点, x 轴的正半轴为极轴建立极坐标系,曲 线 C 的 极 坐 标 方 程 为 ? ? 4 cos ? ,直线 l 的参数方程为

A

BC ?

O
D P

? x ? t? a ? ,则直线 l 将曲线 C 的周长分为 1:5, ? 2 ( t 为参数) t ?y ? ? ? 2
则实数 a ? .

C

B
题(14)图

(16)若关于 x 的不等式 x ? a ? x ?1 ? a 恒成立,则实数 a 的取值范围是



三、解答题:本大题共 6 小题,共 75 分.解答应写出文字说明、证明过程或演算步骤.
(17) (本小题满分 13 分) 已知函数 f ( x) ? sin( x ?

3? ? ) cos( ? x) ? cos x cos(? ? x) . 2 2

(Ⅰ)求 f ( x ) 的最小正周期; (Ⅱ)当 x ? [

? 3?
4 , 4

] ,求 f ( x) 的值域.

(18) (本小题满分 13 分) 某校推行选修数学校本课程,每位同学可以从甲、乙两个科目中人选一个.已知某班第一小组 和第二小组个六位同学的选课情况如下表: 科目甲 第一小组 第二小组 1 2 科目乙 5 4

现从第一小组、第二小组中各选 2 人进行课程交流. (Ⅰ)求选出的 4 人均选修科目乙的概率; (Ⅱ)选出的 4 人中选修科目甲的人数记为 X ,求随机变量 X 的分布列及数学期望.

P
(19) (本小题满分 13 分) 如题(19)图所示,四棱锥 P ? ABCD 中, PA ? 平 面 ABCD , 底 面 ABCD 是 边 长 为 4 的 棱 形 ,

N

?ABC ? 600 , AC 与 BD 交于点 O ,M 、 N 分别

A

D
O M C

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng program mes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For any unit or i ndivi dual, obj ect ively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip betwee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, al ways kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on May to broke more of window gla s s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people manageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e t ube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lear ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the key is i n use , do, li ne. I n pa rti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

B

题(19)图

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI Gener al Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce defens e and army modern, and rich "one countr y, two systems" pra ct ice a nd advance country unified, a nd go peace devel opme nt road, and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" to conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cle does not go int o a link, no leakage of conducting a compre hen sive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht l earni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal i nnovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t hem e, focuse d, result ; often lear n the adva ntages of flexible fi t, form, subtle, conti nue s to

是 OC 、 PD 的中点,异面直线 BD 与 AN 所成角的余弦值为 (Ⅰ)求 PA 的长; (Ⅱ)求二面角 A ? PM ? D 的余弦值.

2 3 . 5

(20) (本小题满分 12 分) 已知函数 f ( x) ? ax ? ln x , g ( x) ? eax ? 2x ,其中 a ? R . (Ⅰ)当 a ? 2 时,求函数 f ( x ) 的极值; (Ⅱ)若存在区间 D ? (0, ??) ,使得 f ( x ) 与 g ( x) 在区间 D 上具有相同的单调性,求 a 的取 值范围. (21) (本小题满分 12 分) 如题(21)图,椭圆 C :

x y ? 2 ? 1(a ? b ? 0) 的离心率 2 a b

2

2

P

y

Q



2 l , F1 、 F2 为其左、右焦点,且 F 1F 2 ? 2 ,动直线 : 2

F1

O

F2

x

y ? kx ? m 与椭圆 C 有且仅有一个公共点.
(Ⅰ)求椭圆 C 的方程; 题(21)图

(Ⅱ)过 F1 、 F2 分别作直线 l 的垂线,垂足分别为 P 、 Q ,求四边形 PF 1F 2Q 面积的最大值.

(22) (本小题满分 12 分)
2 1 ? an a ?1 已知各项都是整数的数列 ?an ? 满足: a1 ? 1 , ? n?1 . 2 1 ? an an

(Ⅰ)求 a2 , a3 , a4 的值,并猜想数列 ?an ? 的通项公式; ( Ⅱ ) 设 数 列 ?an ? 的 前 n 项 和 为 Sn , bn ?

1 (n ? N * ) , 若 A ? bn?1 ? bn?2 ? … ?b2n , 2 Sn

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng programmes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For a ny unit or i ndivi dual, obj ectively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip be twee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, always kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on Ma y to broke more of window glas s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people m anageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e tube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lea r ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the k ey is i n use , do, li ne. I n parti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI General Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce def ens e and army modern, and rich "one countr y, two systems" pra ctice a nd advance country unified, a nd go peace devel opme nt road , and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" t o conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cl e does not go int o a link, no leakage of conducting a compre hensive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht learni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal innovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t heme, focuse d, result ; often lear n the adva ntages of flexible fi t, form , subtle, conti nue s to

B ? cos bn?1 cos bn?2 … cos b2n ,求证:

A ln 4 . ? B 3

2015 年(春)高三考前冲刺测试卷 数学(理工农医类)参考答案
一、选择题:本大题共 10 小题,每小题 5 分,共 50 分. 1~5 BDBAD 6~10 DBBCC

(10)提示:由题知 PA? PB ? PC ? PH ? PB ? PC ? PA? PH

A E D C

? PB ? (PA ? PC) ? PH ? (PC ? PA) ? 0 ? CA ? HB ? 0 ,
同理可得 CB ? HA ? 0 故 H 是 ?ABC 的垂心,如图所示. 设 ?CAD ? ? ,则 AE ? cos? , EH ? sin ? ,

H B

BD ? 2 cos? , DH ? 2 sin ? ,


CD AD 1 ? 2 sin ? ? ? CD ? sin ? ? HE AE cos?

sin ? ? 2 sin 2 ? ? 2 cos? ? ? 3 cos?
?? ?

即 3 cos? ? sin ? ?

? 2 2 ? cos(? ? ) ? 6 2

?
12

?C ?

5? 12 4 4

n i( 又 AD ? 1 ? 2 sin ? ,BD ? 2 cos? , 则 AD ? BD ? 1 ? 2 s

? ? ? ? ) ? 0 ?B ?

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng program mes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For any unit or i ndivi dual, obj ect ively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip betwee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, al ways kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on May to broke more of window gla s s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people manageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e t ube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lear ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the key is i n use , do, li ne. I n pa rti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI Gener al Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce defens e and army modern, and rich "one countr y, two systems" pra ct ice a nd advance country unified, a nd go peace devel opme nt road, and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" to conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cle does not go int o a link, no leakage of conducting a compre hen sive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht l earni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal i nnovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t hem e, focuse d, result ; often lear n the adva ntages of flexible fi t, form, subtle, conti nue s to

从而 A ?

?
3

,于是 ?AOB ? 2?C ?

5? 2? ? , ?BOC ? 2?A ? , ?AOC ? 2?B ? 6 3 2

故 S ?AOB : S ?BOC : S ?AOC ? sin

?? 2? ? 1 3 : sin : sin ? : : 1 ? 1 : 3 : 2 ,选 C. 6 3 2 2 2
(15) ? 1 或 5

二、填空题:本大题共 6 小题,考生作答 5 小题,每小题 5 分,共 25 分. (11) 8 (12) 7 (13) 3 (14) 2

(16) (?? , ] 三、解答题:本大题共 6 小题,共 75 分. (17) (本小题满分 13 分) 解: (Ⅰ) f ( x) ? cos x sin x ? cos2 x ?

1 2

1 1 ? cos2 x 2 ? 1 sin 2 x ? ? sin(2 x ? ) ? 2 2 2 4 2

所以函数 f ( x ) 的最小正周期为 ? ;……6 分 (Ⅱ)x ? [ , 分 (18) (本小题满分 13 分) 解: (Ⅰ) P ?
2 C52 C4 4 ? ? ; ……6 分 2 2 C6 C6 15

? 3? ? ? 5? ? 2 2 ?1 ……13 ] ? 2 x ? ? [ , ] ? sin(2 x ? ) ? [? ,1] ? f ( x) ? [?1, ]. 4 4 4 4 4 4 2 2

(Ⅱ) X 可能的取值为 0,1, 2,3 , P ( X ? 0) ?

2 1 1 1 2 C52C42 4 C 5C 2C 4 ? C 5C 4 22 , , ? P ( X ? 1) ? ? 2 2 C62C62 15 45 C 6C 6

P( X ? 2) ?

1 1 1 2 1 C5 C2C4 ? C52C2 1 2 C5 P ( X ? 3) ? ? , ? 2 2 2 2 C6 C6 9 C 6C 6 45

∴ X 的分布列为:

X P

0

1

2

3

4 15

22 45

2 9

1 45
……13 分

∴ E( X ) ? 0 ?

4 22 2 1 ? 1? ? 2 ? ? 3 ? ? 1 . 15 45 9 45

(19) (本小题满分 13 分) 解: (Ⅰ)如图,以 A 为原点, AD, AP 所在直线为 y, z 轴建立空间直角坐标系. 设 PA ? b, 则 P (0, 0, b), D(0, 4, 0), N (0, 2, ), B(2 3, ?2, 0)

z
P

b 2

N
A D M

b BD ? (?2 3, 6, 0), AN ? (0, 2, ), 2
B

O

y

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng programmes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For a ny unit or i ndivi dual, obj ectively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip be twee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, always kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on Ma y to broke more of window glas s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people m anageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e tube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lea r ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the k ey is i n use , do, li ne. I n parti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

C

x

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI General Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce def ens e and army modern, and rich "one countr y, two systems" pra ctice a nd advance country unified, a nd go peace devel opme nt road , and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" t o conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cl e does not go int o a link, no leakage of conducting a compre hensive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht learni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal innovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t heme, focuse d, result ; often lear n the adva ntages of flexible fi t, form , subtle, conti nue s to



12 48 ? 4 ? b 4
2

?

2 3 ? b ? 3 ; ……6 分 5
3 3 3 , ,0) 2 2

(Ⅱ)由题意知 BD ? (?2 3,6,0) 是平面 OMP 的一个法向量, M ( 设平面 PMD 的法向量为 n ? ( x, y, z) ,由 ?

? ?n ? PD ? 0

? ?n ? PM ? 0 BD ? n 1 设二面角 A ? PM ? D 的大小为 ? ,则 cos ? ? ? . | BD | ? | n | 5

?n?(

5 3 ,3, 4) 3
……13 分

(20) (本小题满分 12 分) 解: (Ⅰ)当 a ? 2 时, f ?( x) ? 2 ? 单调递增; 所以, f ( x ) 在 x ? (Ⅱ) f ?( x) ? a ?

1 1 1 ,故当 x ? (0, ) 时, f ( x ) 单调递减;当 x ? ( , ??) 时, f ( x ) x 2 2

1 1 处取得极小值 f ( ) ? 1 ? ln 2 ,无极大值; 2 2

……5 分

1 , g ?( x) ? aeax ? 2 x

当 a ? 0 时, g ?( x) ? 0 ,即 g ( x) 在 R 上单调递增,而 f ( x ) 在 ( , ??) 上单调递增, 故必存在 D ? (0, ??) ,使得 f ( x ) 与 g ( x) 在 D 上单调递增; 当 a ? 0 时, f ?( x) ? ? 递增, 故不存在满足条件的区间 D ; 当 a ? 0 时, f ?( x) ? a ? 上单调递减,

1 a

1 ? 0 ,故 f ( x) 在 (0, ??) 上单调递减,而 g ( x) 在 (0, ??) 上单调 x

1 1 2 ? 0 ,即 f ( x) 在 (0, ??) 上单调递减,而 g ( x) 在 (??, ln(? )) x a a

1 2 ( ln(? ), ??) 上单调递增,若存在存在 D ? (0, ??) ,使得 f ( x) 与 g ( x) 在 D 上单调性 a a
相同,则有

1 2 ln(? ) ? 0 ,解得 a ? ?2 ; a a
综上, a ? 0 或 a ? ?2 . (21) (本小题满分 12 分) ……12 分

x2 2 C ? y 2 ? 1;……4 分 解: (Ⅰ)由题知 c ? 1, e ? ,故 a ? 2, b ? 1,故椭圆 的方程为 2 2
deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng program mes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For any unit or i ndivi dual, obj ect ively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip betwee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, al ways kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on May to broke more of window gla s s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people manageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e t ube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lear ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the key is i n use , do, li ne. I n pa rti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI Gener al Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce defens e and army modern, and rich "one countr y, two systems" pra ct ice a nd advance country unified, a nd go peace devel opme nt road, and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" to conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cle does not go int o a link, no leakage of conducting a compre hen sive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht l earni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal i nnovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t hem e, focuse d, result ; often lear n the adva ntages of flexible fi t, form, subtle, conti nue s to

(Ⅱ)当 k ? 0 时, S四边形PF1F2Q ? 2 ; 当 k ? 0 时, 令 | PF 则 d1 ?| 1 |? d1 ,| PF 2 |? d2 ,

?k ? m 1? k 2

|, d 2 ?|

k?m 1? k 2

| PQ |?| |,

d1 ? d 2 |. k

? y ? kx ? m ? 由 ? x2 得 (1 ? 2k 2 ) x2 ? 4kmx ? 2m2 ? 2 ? 0 2 ? ? y ?1 ?2
由题知 ? ? 16k 2 m2 ? 4(1 ? 2k 2 )(2m2 ? 2) ? 0 即 m2 ? 1 ? 2k 2 所以 S四边形PF1F2Q ? 所以 S四边形PF1F2Q ?|
2 d 2 ? d2 1 2m (d1 ? d 2 )? | PQ |?| 1 |?| | ,又 m2 ? 1 ? 2k 2 ,故 | m |? 1 2 2 2k 1? k

2m 4 |= ? 2; 2 1 1? k |m|? |m|
……12 分

综上,当 k ? 0 时, S四边形PF1F2Q 取得最大值 2 . (22) (本小题满分 12 分)

解: (Ⅰ)由 an ? 0 ? 1 ? an?12 ? 0 ? 0 ? an?1 ? 1, ? a1 ? 1 ,当 n ≥ 2 时, 0 ? an ? 1 由题知

1 1 1 1 1 ? an ?1 ? an ? ? ( ? an ?12 ) ? ( 2 ? an 2 ) ? 4 ,而 a12 ? 2 ? 2, 2 an?1 an an ?1 an a1

即数列 ?

? 1 ? 1 2 ? an 2 ? 是以 2 为首项、 4 为公差的等差数列,? 2 ? an ? 4n ? 2 2 an ? an ?

即 an ? n ? n ? 1 ; (也可先猜出通项,再用数学归纳法证明! )……5 分 (Ⅱ) Sn ? a1 ? a2 ?

? an ? ( 1 ? 0) ? ( 2 ? 1) ?

? ( n ? n ? 1) ? n

? bn ?

1 1 1 1 1 1 1 ? ??? cos ? cos ,A? , B ? cos n n ?1 n ? 2 2n n ?1 n?2 2n 1 ?x ?1 ? , ? f ( x) 在 x ?1 x ?1

x ? 1) ≤ x : 令 f ( x) ? ln ( x ? 1) ? x , 则 f ?( x) ? 先 证 ln (

(?1,0) 上单增,

在 (0,??) 上单减,故 f ( x ) ≤ f (0) ? 0 ,即当 x ? 0 时, ln(x ? 1) ? x ; 令x??

1 1 1 1 n (n ? 1) ,则有 ln(1 ? ) ? ? 即 ? ln n n n n n ?1

故有 A ?

1 1 1 n ?1 n?2 2n ? ??? ? ln ? ln ? ? ? ln ? ln 2 ; n ?1 n ? 2 2n n n ?1 2n ? 1

先证当 x ? (0,

?

) 时,sin x ? x :令 g (x ) ? sin x ? x(0 ? x ? ) ? g'( x ) ? cos x ? 1 ? 0 2 2

?

deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng programmes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For a ny unit or i ndivi dual, obj ectively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip be twee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, always kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on Ma y to broke more of window glas s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people m anageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e tube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lea r ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the k ey is i n use , do, li ne. I n parti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four

guarantee for t he great struggl e. T his as pe cts XI Ge neral Se cretary of s pee ch mai n including exer cise t hrift, against extrava gance mass l ine i s party of lifeline a nd fundame ntal work route accurate gras p party of mass line educati on practi ce activitie s of guideli ne a nd target re quireme nts set a nd develop "three stri ct three real" of style put power shut into system of cag e in usi ng hist ory wis dom a dvance anti -corruption constr ucti on i n-dept h adva nce style cl ean g overnment and anti -corrupti on struggle devel op nail nail of spirit, a Z ha ng good of blue print w orked t o... 9. ot her as pe cts. 1 8 big yilai, XI General Secretary al so re spe ctively on di plomati c, and militar y, and e col ogical construction, as pe cts publi she d ha s important s pee ch, covers has construction e col ogical civilizati on, and adva nce def ens e and army modern, and rich "one countr y, two systems" pra ctice a nd advance country unified, a nd go peace devel opme nt road , and pr omoted bui ldi ng new powers relati ons hip, and go g ood around di plomati c work, and strengt heni ng and developing countries soli darity cooperation, a nd a ctive participati on mult ilateral affairs, and s cience of thi nking a nd w ork method, many as pe cts. XI Jinpi ng, Se cretary of a series of important s pee ches , and further e nrich and devel op the party's the ory, li ne, principle s and poli cies , the party puts forwar d new re quireme nts for more contemporary features, the latest achieveme nt of Marxism in China , is a gui de to persisting a nd developing socialism with Chi nese chara cteristics. Four met hods. To address t he relations hip between compr ehe nsive a nd focuse d on sci ence. I n the pr oce ss of learning, we shoul d follow a s a good study and carry out the "wise men" t o conduct a compre hensive collaborative learni ng; a nd wit h their own j obs, focus research and understa ndi ng spirit , grasp the pote ntial requirements. F or example, every party member shoul d be a ccording t o the various bra nches of learning program, an arti cl e does not go int o a link, no leakage of conducting a compre hensive study, a nd combi ned with their own dutie s and responsibil ities, be focused a nd targeted G eos cie nce . Like, lea ders to highlig ht learni ng XI on r uling a cting political k now of deep l ove of cut dry in practice go in forefront of river new lang uage out poverty XI on coor dinati on adva nce "four a ful l" strategy layout dis cus ses excer pts XI on full dee pe ning reform dis cusses excerpts XI on full law ruli ng di scusse s excerpts 18 big yilai XI on major e conomi c problem dis cusses ex cerpts, di sci pline t o highlig ht learni ng XI on stri ct party of di sci pline a nd r ules di scuss es excer pts XI Ji nping, on the constructi on of clean a nd honest Gover nment a nd fight against corr upti on di scusse d excer pts, technology to highlig ht the learning of the XI Jinping on technologi cal innovation and di s cus ses excer pts, XI Jinpi ng, e ducati on should highlig ht the important excer pts of work on educati on a nd s o on. To address the relation betwee n stage a nd often scie nce . Phase ha s the a dvantage of time to focus on fast, to hig hlight the t heme, focuse d, result ; often lear n the adva ntages of flexible fi t, form , subtle, conti nue s to

? ? ? g ( x ) 在 (0, ) 上单减,故 g ( x ) ? g (0) ? 0 ,即 sin x ? x 在 (0, ) 上成立; 2 2
令x?

1 1 1 1 (n ? 1)( n ? 1) 1 (n ? N * ) ,则 sin 2 ? 2 ? cos 2 ? 1 ? 2 ? n n n n n n2

故B ?
2

n(n ? 2) (n ? 1)(n ? 3) (2n ? 1)(2n ? 1) 2n ? 1 3 3 ≥ ,? B ? ; ? ??? ? 2 2 2 (n ? 1) (n ? 2) ( 2n) 2n ? 2 4 2
……12 分

综上,

A ln 2 ln 4 ? ? . B 3 3 2

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deepen. I n Ge neral, periodic hig h pri ority on l earni ng, easy to gras p and pra ctice: re curre nt learni ng factors, l ong time, prone to "sluggi sh". Le arni ng program mes are expli citly required to l earn e ducati on i s not a n event, but to highlig ht the normal educati on, differentiated levels, heart, cat ch a fine practice, the real party's ide ologi cal and political construction in the everyday, often. T his requires t hat we do a good job phase focuse d lear ning ba sed on k nowle dge contests , comme nts on rewards i n the form, pay spe cial attention to re curring studi es. To ha ndle the relati ons hip betwee n s olid s trong to learn a nd a l ot to lear n. For any unit or i ndivi dual, obj ect ively s peaki ng, in t he proces s of carryi ng out the party Constit ution Party rules a nd spirit, t here is a pr obl em with strong and weak, w hich we ne ed to pay atte ntion t o the a ctual lear ning conte nt, and ha ndl e the relati ons hip betwee n soli d strong to learn a nd a l ot to learn. On one ha nd, we m ust always kee p a hum ble attitude, good deal, Continue the hardeni ng. The other hand, al ways kee p the spirit of energetic, pegged to t he weak li nk to find 动 活 益 公 项 各 的 外 内 体 文 术 与 参 过 通 以 可 难 济 经 校 我 ”。 ·屋 梦 “衍 立 设 特 会 社 报 回 心 爱 递 传 奖 获 、 源 思 受 大 广 导 引 和 教 能 功 人 育 挥 发 , 作 工 生 学 庭 家 困 贫 助 资 好 做 步 一 进 为 gaps, fill the short Boar d. Short Board i ssue s shoul d not be underestimated, t he saying g oes, have short Board, a dd a short. Thi s tells us, there are weakne sses shortcomi ngs and do not be afraid, fear is a blind eye and not to repai r, the re sult is poor is wor se and the w eak weaker. United States pol itics home zham usi, a nd Wil son and preve ntion crime lear n experts qiaoz hikaili n pr opose d has a famous of br oken wi ndow the ory, that, if a buildi ng House has a fan wi ndow of glas s broke n ha s, and this fan Wi ndows no get timely repai r, ot hers on May to broke more of window gla s s, time a long , these damaged of wi ndow on to pe opl e ca used a dis orde r, and matter of feel, results i n this mas s errors t hink no attenti on, a nd no management of atmos pher e Xia, some bad culture , and violations behavi or on will br eedi ng and sprea d. Reality life in the i s such, clea n of wall Sha ng, s udde nly wa s poste d ha s a Zha ng ad, if di dn't people manageme nt, not out days this w all Sha ng on will appeare d greatly small many of advertis ing; private take mess built phenomenon i s so, began circle a small bl ock to built a small she d put t hings, if di dn't people timely stop, he on dare built a hut live people, time l ong ha s di dn't pe opl e t ube, wants t o tube S hi on difficult has. Therefore, the soli d strong is importa nt, a lot to lear n is als o important. Third, key, gras p the le arning obj ective of educati on i s to train a qualif ied party member "two" study and education to its core es sence is lear ning a nd doi ng. Lear ning a nd doi ng are mutually rei nforci ng, if opti cal ca n't do, st udy leave , real learni ng defici ency, w hile sw eating, wi nd a nd wate r, "one fis hing w hite" be came "fake words and not the mule s". Lear ning party rules di d not com ply with the party Constituti on, a ddre ss the le arning series i s not used, instea d, learn a nd do, imagine this "lear ning", how do you meet t he eligi bility requirements of party members. T herefore, the "two" ba sic le arning, the key is i n use , do, li ne. I n pa rti cula r, is a qualified party members to gras p the following thre e poi nts. To stre ngthen "four


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