闂傚倸鍊搁崐鎼佸磹閹间礁纾归柟闂寸绾惧綊鏌熼梻瀵割槮缁炬儳缍婇弻鐔兼⒒鐎靛壊妲紒鐐劤濠€閬嶅焵椤掑倹鍤€閻庢凹鍙冨畷宕囧鐎c劋姹楅梺鍦劋閸ㄥ綊宕愰悙宸富闁靛牆妫楃粭鍌滅磼閳ь剚绗熼埀顒€鐣峰⿰鍫晣闁绘垵妫欑€靛矂姊洪棃娑氬婵☆偅顨嗛幈銊槾缂佽鲸甯¢幃鈺呭礃閼碱兛绱濋梻浣虹帛娓氭宕抽敐鍡樺弿闁逞屽墴閺屾洟宕煎┑鍥舵¥闂佸憡蓱閹瑰洭寮婚埄鍐ㄧ窞閻忕偞鍨濆▽顏呯節閵忋垺鍤€婵☆偅绻傞悾宄扳攽閸♀晛鎮戦梺绯曞墲閸旀帞鑺辨繝姘拺闁告繂瀚埀顒佹倐閹ê鈹戠€e灚鏅滃銈嗗姂閸婃澹曟總绋跨骇闁割偅绋戞俊鐣屸偓瑙勬礀閻ジ鍩€椤掑喚娼愭繛鍙夅缚閺侇噣骞掑Δ瀣◤濠电娀娼ч鎰板极閸曨垱鐓㈡俊顖欒濡插嘲顭跨憴鍕婵﹥妞藉畷銊︾節閸曨厾绐楅梻浣呵圭€涒晜绻涙繝鍥х畾閻忕偠袙閺嬪酣鏌熼幆褜鍤熼柛姗€浜跺娲传閸曨剙鍋嶉梺鍛婃煥閻倿骞冨鈧幃鈺呮偨閻㈢绱查梻浣虹帛閻熴垽宕戦幘缁樼厱闁靛ǹ鍎抽崺锝団偓娈垮枛椤攱淇婇幖浣哥厸闁稿本鐭花浠嬫⒒娴e懙褰掑嫉椤掑倻鐭欓柟杈惧瘜閺佸倿鏌ㄩ悤鍌涘婵犵數濮烽弫鍛婃叏閻戣棄鏋侀柛娑橈攻閸欏繘鏌i幋锝嗩棄闁哄绶氶弻娑樷槈濮楀牊鏁鹃梺鍛婄懃缁绘﹢寮婚敐澶婄闁挎繂妫Λ鍕⒑閸濆嫷鍎庣紒鑸靛哺瀵鎮㈤崗灏栨嫽闁诲酣娼ф竟濠偽i鍓х<闁诡垎鍐f寖缂備緡鍣崹鎶藉箲閵忕姭妲堥柕蹇曞Х椤撴椽姊洪崫鍕殜闁稿鎹囬弻娑㈠Χ閸涱垍褔鏌$仦鍓ф创濠碉紕鍏橀、娆撴偂鎼存ɑ瀚介梻鍌欐祰濡椼劎绮堟担璇ユ椽顢橀姀鐘烘憰闂佸搫娴勭槐鏇㈡偪閳ь剟姊洪崫鍕窛闁稿⿴鍋婃俊鐑芥晜鏉炴壆鐩庨梻浣瑰濡線顢氳閳诲秴顓兼径瀣幍濡炪倖姊婚悺鏂库枔濠婂應鍋撶憴鍕妞ゃ劌妫楅銉╁礋椤掑倻鐦堟繛杈剧到婢瑰﹤螞濠婂牊鈷掗柛灞捐壘閳ь剟顥撶划鍫熺瑹閳ь剟鐛径鎰伋閻℃帊鐒﹀浠嬪极閸愵喖纾兼慨妯诲敾缁卞崬鈹戦悩顔肩伇闁糕晜鐗犲畷婵嬪即閵忕姴寮烽梺闈涱槴閺呮粓鎮¢悢鍏肩厵闂侇叏绠戦弸娑㈡煕閺傛鍎旈柡灞界Ч閺屻劎鈧綆浜炴导宀勬⒑鐠団€虫灈缂傚秴锕悰顔界瑹閳ь剟鐛幒妤€绠f繝鍨姉閳ь剝娅曠换婵嬫偨闂堟稐绮堕梺鐟板暱缁绘ê鐣峰┑鍡忔瀻闁规儳鐤囬幗鏇㈡⒑缂佹ɑ鈷掗柛妯犲懐鐭嗛柛鏇ㄥ灡閻撳繘鏌涢锝囩畺妞ゃ儲绮嶉妵鍕疀閵夛箑顏�
(Ⅱ)求的取值范圍. 查看更多

 

題目列表(包括答案和解析)

一、選擇題(每小題5分,共50分)

6ec8aac122bd4f6e

二、填空題(每小題4分,共28分)

6ec8aac122bd4f6e

三、解答題

18.解:(Ⅰ)由已有

6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e

                                    (4分)

 

6ec8aac122bd4f6e

                                            (6分)

 

(Ⅱ)由(1)6ec8aac122bd4f6e6ec8aac122bd4f6e                                 (8分)

所以6ec8aac122bd4f6e              (10分)

6ec8aac122bd4f6e                                                      (12分)

6ec8aac122bd4f6e

6ec8aac122bd4f6e                                  (14分)

 

19.解:(Ⅰ)同學(xué)甲同學(xué)恰好投4次達標(biāo)的概率6ec8aac122bd4f6e           (4分)

(Ⅱ)6ec8aac122bd4f6e可取的值是6ec8aac122bd4f6e

6ec8aac122bd4f6e                                              (6分)

6ec8aac122bd4f6e                                            (8分)

6ec8aac122bd4f6e                                              (10分)

6ec8aac122bd4f6e的分布列為

6ec8aac122bd4f6e

3

4

5

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

                                                                      (12分)

所以6ec8aac122bd4f6e的數(shù)學(xué)期望為6ec8aac122bd4f6e                   (14分)

 

20.解:(Ⅰ)∵PA⊥底面ABCD,BC6ec8aac122bd4f6e平面AC,∴PA⊥BC

∵∠ACB=90°,∴BC⊥AC,又PA∩AC=A,∴BC⊥平面PAC                (4分)

 

(Ⅱ)取CD的中點E,則AE⊥CD,∴AE⊥AB,又PA⊥底面ABCD,∴PA⊥AE

建立如圖所示空間直角坐標(biāo)系,則

A(0,,0,0),P(0,0,6ec8aac122bd4f6e),C(6ec8aac122bd4f6e,0),D(6ec8aac122bd4f6e,0)

6ec8aac122bd4f6e6ec8aac122bd4f6e,6ec8aac122bd4f6e,6ec8aac122bd4f6e                  (6分)

易求6ec8aac122bd4f6e為平面PAC的一個法向量.

6ec8aac122bd4f6e為平面PDC的一個法向量                                  (9分)

∴cos6ec8aac122bd4f6e

故二面角D-PC-A的正切值為2.  (11分)

(Ⅲ)設(shè)6ec8aac122bd4f6e,則

   6ec8aac122bd4f6e,

解得點6ec8aac122bd4f6e,即6ec8aac122bd4f6e   (13分)

6ec8aac122bd4f6e6ec8aac122bd4f6e(不合題意舍去)或6ec8aac122bd4f6e

所以當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e的中點時,直線6ec8aac122bd4f6e與平面6ec8aac122bd4f6e所成角的正弦值為6ec8aac122bd4f6e   (15分)

 

21.解:(Ⅰ)設(shè)直線6ec8aac122bd4f6e的方程為:6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e,所以6ec8aac122bd4f6e的方程為6ec8aac122bd4f6e                     (4分)

6ec8aac122bd4f6e6ec8aac122bd4f6e點的坐標(biāo)為6ec8aac122bd4f6e.

可求得拋物線的標(biāo)準(zhǔn)方程為6ec8aac122bd4f6e.                                       (6分)

(Ⅱ)設(shè)直線6ec8aac122bd4f6e的方程為6ec8aac122bd4f6e,代入拋物線方程并整理得6ec8aac122bd4f6e    (8分)     

設(shè)6ec8aac122bd4f6e6ec8aac122bd4f6e

設(shè)6ec8aac122bd4f6e,則6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e                                      (11分)

當(dāng)6ec8aac122bd4f6e時上式是一個與6ec8aac122bd4f6e無關(guān)的常數(shù).

所以存在定點6ec8aac122bd4f6e,相應(yīng)的常數(shù)是6ec8aac122bd4f6e.                                     (14分)

 

22.解:(Ⅰ)當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e              (2分)

6ec8aac122bd4f6e6ec8aac122bd4f6e上遞增,在6ec8aac122bd4f6e上遞減

所以6ec8aac122bd4f6e在0和2處分別達到極大和極小,由已知有

6ec8aac122bd4f6e6ec8aac122bd4f6e,因而6ec8aac122bd4f6e的取值范圍是6ec8aac122bd4f6e.                                   (4分)

(Ⅱ)當(dāng)6ec8aac122bd4f6e時,6ec8aac122bd4f6e6ec8aac122bd4f6e

6ec8aac122bd4f6e可化為6ec8aac122bd4f6e6ec8aac122bd4f6e,記6ec8aac122bd4f6e

6ec8aac122bd4f6e                                        (7分)

6ec8aac122bd4f6e6ec8aac122bd4f6e,

6ec8aac122bd4f6e6ec8aac122bd4f6e上遞減,在6ec8aac122bd4f6e上遞增.

6ec8aac122bd4f6e

從而6ec8aac122bd4f6e上遞增

因此6ec8aac122bd4f6e6ec8aac122bd4f6e                           (10分)

(Ⅲ)假設(shè)6ec8aac122bd4f6e6ec8aac122bd4f6e,即6ec8aac122bd4f6e6ec8aac122bd4f6e=6ec8aac122bd4f6e

6ec8aac122bd4f6e,

6ec8aac122bd4f6e                                     (12分)

6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e(x)=0的兩根可得,6ec8aac122bd4f6e

從而有6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e≥26ec8aac122bd4f6e,這與6ec8aac122bd4f6e<26ec8aac122bd4f6e矛盾.                                

故直線6ec8aac122bd4f6e與直線6ec8aac122bd4f6e不可能垂直.                                               (15分)

 


同步練習(xí)冊答案
闂傚倸鍊搁崐鎼佸磹閹间礁纾归柟闂寸绾惧綊鏌熼梻瀵割槮缁炬儳缍婇弻鐔兼⒒鐎靛壊妲紒鐐劤缂嶅﹪寮婚敐澶婄闁挎繂鎲涢幘缁樼厱闁靛牆鎳庨顓㈡煛鐏炶鈧繂鐣烽锕€唯闁挎棁濮ら惁搴♀攽閻愬樊鍤熷┑顔炬暬閹虫繃銈i崘銊у幋闂佺懓顕崑娑氱不閻樼粯鈷戠紒瀣皡閺€缁樸亜閵娿儲顥㈡鐐茬墦婵℃瓕顦柛瀣崌濡啫鈽夊▎蹇旀畼闁诲氦顫夊ú鏍ь嚕閸洖绠為柕濞垮労濞撳鎮归崶顏勭处濠㈣娲熷缁樻媴閾忕懓绗℃繛鎾寸椤ㄥ﹤鐣烽弶搴撴婵ê褰夌粭澶娾攽閻愭潙鐏﹂懣銈嗕繆閹绘帞澧涚紒缁樼洴瀹曞崬螣閸濆嫷娼旀俊鐐€曠换鎺楀窗閺嵮屾綎缂備焦蓱婵挳鏌ら幁鎺戝姢闁靛棗锕娲閳哄啰肖缂備胶濮甸幑鍥偘椤旇法鐤€婵炴垶鐟﹀▍銏ゆ⒑鐠恒劌娅愰柟鍑ゆ嫹 闂傚倸鍊搁崐鎼佸磹閹间礁纾归柟闂寸绾惧綊鏌熼梻瀵割槮缁炬儳缍婇弻鐔兼⒒鐎靛壊妲紒鐐劤缂嶅﹪寮婚悢鍏尖拻閻庨潧澹婂Σ顔剧磼閻愵剙鍔ょ紓宥咃躬瀵鎮㈤崗灏栨嫽闁诲酣娼ф竟濠偽i鍓х<闁绘劦鍓欓崝銈囩磽瀹ュ拑韬€殿喖顭烽幃銏ゅ礂鐏忔牗瀚介梺璇查叄濞佳勭珶婵犲伣锝夘敊閸撗咃紲闂佺粯鍔﹂崜娆戠矆閸愨斂浜滈柡鍥ф濞层倝鎮″鈧弻鐔告綇妤e啯顎嶉梺绋款儐閸旀瑩寮诲☉妯锋瀻闊浄绲炬晥闂備浇顕栭崰妤呮偡瑜忓Σ鎰板箻鐎涙ê顎撻梺鍛婄箓鐎氱兘鍩€椤掆偓閻倿寮诲☉銏犖╅柕澹啰鍘介柣搴㈩問閸犳牠鈥﹂柨瀣╃箚闁归棿绀侀悡娑㈡煕鐏炲墽鐓紒銊ょ矙濮婄粯鎷呴崨闈涚秺瀵敻顢楅崒婊呯厯闂佺鎻€靛矂寮崒鐐寸叆闁绘洖鍊圭€氾拷