❶ 涓夊勾绾уゥ鏁伴樺強绛旀堝湪鏁板垪1銆2銆3銆4銆3銆4銆5銆6銆5銆6銆7銆8銆7銆8銆9銆10銆9銆10路路路路路路涓锛岀201
鍘熸暟鐨勬帓鍒楁柟寮忥細
锛1锛2锛3锛4锛夛紙3锛4锛5锛6锛夛紙5锛6锛7锛8锛夈傘傘傘
闄や簡绗涓缁勫栵紝鍚庝竴缁勯兘鏄鐢ㄤ簡鍓嶄竴缁勭殑鍚庝袱浣嶇劧鍚庡姞涓嬩袱涓杩炵画鐨勮嚜鐒舵暟鏋勬垚銆傚洜姝や粠绗浜岀粍寮濮嬶紝姣忎竴缁勫疄闄呭氬炰袱涓鏂扮殑杩炵画鑷鐒舵暟銆
201=4*50+1
绗201椤规槸绗51缁勭殑绗涓涓锛屾瘡涓缁勭殑绗涓涓鐨勫肩瓑浜庡墠涓缁勭殑绗涓変釜锛屽洜姝ゆ湁绗201椤圭殑鍊兼槸锛4+2*48+1=101
鍥犳ょ201椤圭殑鍊兼槸101
❷ 涔濆勾绾ф暟瀛︽湡鏈娴嬭瘯棰橈紝鍦板潃銆
涔濆勾绾ф暟瀛︿笂瀛︽湡鏈熸湯澶嶄範璁缁冮
(鏈璁缁冮樺垎涓変釜澶ч橈紝婊″垎120鍒嗭紝璁缁冩椂闂村叡120鍒嗛挓)
涓銆侀夋嫨棰橈紙鏈澶ч10棰橈紝鍏30鍒嗭級锛
1锛庡凡鐭 = 锛屽叾涓璦鈮0锛屽垯b婊¤冻鐨勬潯浠舵槸锛 锛
A锛巄<0 B锛巄鈮0 C锛巄蹇呴』绛変簬闆 D锛庝笉鑳界‘瀹
2锛庡凡鐭ユ姏鐗╃嚎鐨勮В鏋愬紡涓簓= -锛坸-3锛2+1锛屽垯瀹冪殑瀹氱偣鍧愭爣鏄锛 锛
A锛庯紙3锛1锛 B锛庯紙-3锛1锛 C锛庯紙3锛-1锛 D锛庯紙1锛3锛
3锛庝笅鍒椾氦閫氭爣蹇椾腑锛屾棦鏄杞村圭О鍥惧舰鍙堟槸涓蹇冨圭О鍥惧舰鐨勬槸锛 锛
4锛庡凡鐭ワ紙1-x锛2 + =0锛屽垯x+y鐨勫间负锛 锛
A锛1 B锛2 C锛3 D锛4
5锛庢牎杩愬姩浼氫笂锛屽皬鏄庡悓瀛︽幏鍑虹殑閾呯悆鍦ㄥ満鍦颁笂鐮稿嚭涓涓鍧戝彛鐩村緞涓10cm锛屾繁涓2cm鐨勫皬鍧戯紝鍒欒ラ搮鐞冪殑鐩村緞绾︿负锛 锛
A锛10cm B锛14.5cm C锛19.5cm D锛20cm
6锛庡湪鏂板勾鑱旀浼氫笂锛屼節骞寸骇锛1锛夌彮鐨勭彮濮旇捐′簡涓涓娓告垙锛屽苟缁欎簣鑳滃埄鑰呯敳銆佷箼涓ょ嶄笉鍚屽栧搧涓鐨勪竴绉. 鐜板皢濂栧搧鍚嶇О鍐欏湪瀹屽叏鐩稿悓鐨勫崱鐗囦笂锛岃儗闈㈡湞涓婃暣榻愭帓鍒楋紝濡傚浘鎵绀. 鑻ラ槾褰遍儴鍒嗘斁缃鐨勬槸鍐欐湁涔欑嶅栧搧鐨勫崱鐗囷紝鍒欒儨鍒╄呭皬鍒氬悓瀛﹀緱鍒颁箼绉嶅栧搧鐨勬傜巼鏄锛 锛
A锛 B锛 C锛 D锛
7锛庢煇鍩庡競2007骞村簳宸茬豢鍖栭潰绉300鍏椤凤紝缁忚繃涓ゅ勾缁垮寲锛岀豢鍖栭潰绉閫愬勾澧炲姞锛屽埌2009骞村簳澧炲姞鍒363鍏椤. 璁剧豢鍖栭潰绉骞冲潎姣忓勾鐨勫為暱鐜囦负x锛岀敱棰樻剰锛屾墍鍒楁柟绋嬫ｇ‘鐨勬槸锛 锛
A锛300锛1+x锛=363 B锛300锛1+x锛2 =363
C锛300锛1+2x锛=363 D锛300锛1-x锛2 =363
8锛庡凡鐭ュ叧浜巟鐨勪竴鍏冧簩娆℃柟绋媥2 +mx+4=0鏈変袱涓姝ｆ暣鏁版牴锛屽垯m鍙鑳藉彇鐨勫间负锛 锛
A锛巑>0 B锛巑>4 C锛-4锛-5 D锛4锛5
9锛庡傚浘锛屽皬鏄庝负鑺傜渷鎼杩愬姏姘旓紝鎶婁竴涓妫遍暱涓1m鐨勬ｆ柟浣撴湪绠卞湪鍦伴潰涓婄敱璧峰嬩綅缃娌跨洿绾縧涓嶆粦鍔ㄧ殑缈绘粴锛岀炕婊氫竴鍛ㄥ悗锛屽師鏉ヤ笌鍦伴潰鎺ヨЕ鐨勯潰ABCD鍙堣惤鍥炲埌鍦伴潰锛屽垯鐐笰1鎵璧拌矾寰勭殑闀垮害涓猴紙 锛
A锛庯紙 锛塵 B锛庯紙 锛塵
C锛庯紙 锛塵 D锛庯紙 锛塵
10锛庡傚浘锛屽凡鐭ョ洿绾緽C鍒団姍O浜庣偣C锛孭D涓衡姍O鐨勭洿寰勶紝BP鐨勫欢闀跨嚎涓嶤D鐨勫欢闀跨嚎浜や簬鐐笰锛屸垹A=28掳锛屸垹B=26掳锛屽垯鈭燩DC绛変簬锛 锛
A锛34掳 B锛36掳 C锛38掳 D锛40掳
浜屻佸～绌洪橈紙鏈澶ч6灏忛橈紝鍏18鍒嗭級锛
11锛庡凡鐭 =1.414锛屽垯 锛堜繚鐣欎袱涓鏈夋晥鏁板瓧锛.
12锛庤嫢涓ゅ渾鐨勫崐寰勫垎鍒鏄鏂圭▼x2-3x+2=0鐨勪袱鏍癸紝涓斾袱
鍦嗙浉浜わ紝鍒欎袱鍦嗗渾蹇冭窛d鐨勫彇鍊艰寖鍥存槸 .
13锛庤嫢鍑芥暟y=ax2+3x+1涓巟杞村彧鏈変竴涓浜ょ偣锛屽垯a鐨勫间负 .
14锛庡傚浘锛屽凡鐭ュぇ鍗婂渾O1涓庡皬鍗婂渾O2鍐呭垏浜庣偣B锛屽ぇ鍗婂渾鐨勫鸡MN鍒囧皬鍗婂渾浜庣偣D锛岃嫢MN鈭AB锛屽綋MN=4鏃讹紝鍒欐ゅ浘涓鐨勯槾褰遍儴鍒嗙殑闈㈢Н鏄 .
15锛庡浗瀹朵负榧撳姳娑堣垂鑰呭悜鍟嗗剁储瑕佸彂绁ㄦ秷璐癸紝鍒跺畾浜嗕竴瀹氱殑濂栧姳鎺鏂斤紝鍏朵腑瀵100鍏冪殑鍙戠エ锛堝栬備竴鏍凤紝濂栧姳閲戦濈敤瀵嗗皝绛惧皝鐩栵級鏈夊栭噾5鍏冿紝濂栭噾10鍏冿紝濂栭噾50鍏冨拰璋㈣阿绱㈣佸洓绉嶏紝鐜版煇鍟嗗舵湁1000寮100鍏冪殑鍙戠エ锛岀粡绋庡姟閮ㄩ棬鏌ヨ瘉锛岃繖1000寮犲彂绁ㄧ殑濂栧姳鎯呭喌濡備笅琛, 鏌愭秷璐硅呮秷璐100鍏冿紝鍚戣ュ晢瀹剁储瑕佸彂绁ㄤ竴寮狅紝涓10鍏冨栭噾鐨勬傜巼鏄 .
濂栭」 5鍏 10鍏 50鍏 璋㈣阿绱㈣
鏁伴噺 50寮 20寮 10寮 鍓╀綑閮ㄥ垎
16锛庡傚浘锛孉B涓衡姍O鐨勭洿寰勶紝CD涓哄鸡锛孋D鈯AB浜嶦锛屽傛灉CD=6锛孫E=4锛岄偅涔圓C鐨勯暱涓 .
涓夈佽В绛旈橈紙鏈澶ч8棰橈紝鍏72鍒嗭級锛
17锛庯紙6鍒嗭級璁＄畻锛 .
18锛庯紙6鍒嗭級瑙ｆ柟绋嬶細x2-6x+9=锛5-2x锛2.
19锛庯紙8鍒嗭級鍏堝寲绠锛屽啀姹傚硷細
锛屽叾涓璦鏄鏂圭▼2x2-x-3=0鐨勮В.
20锛庯紙8鍒嗭級濡傚浘锛屽凡鐭ヤ笁涓鍚屽績鍦嗭紝绛夎竟涓夎掑舰ABC鐨勪笁涓椤剁偣鍒嗗埆鍦ㄤ笁涓鍦嗕笂锛岃蜂綘鎶婅繖涓涓夎掑舰缁曠潃鐐筄椤烘椂閽堟棆杞120掳锛岀敾鍑衡柍A/B/C/. 锛堢敤灏鸿勪綔鍥撅紝涓嶅啓鐢绘硶锛屼繚鐣欎綔鍥剧棔杩癸級
21锛庯紙10鍒嗭級涓涓瀵嗗皝鐨勫彛琚嬩腑鏈変袱绉嶅彧鏈夐滆壊涓嶅悓鐨勭孩鐞儀涓锛岄粍鐞儁涓锛屼粠鍙ｈ嬩腑闅忔満鍦板彇鍑轰竴涓鐞冿紝鑻ュ畠鏄绾㈢悆鐨勬傜巼涓 .
锛1锛夋眰y涓巟鐨勫嚱鏁板叧绯诲紡锛
锛2锛夎嫢浠庡彛琚嬩腑鎷垮嚭6涓绾㈢悆鍚庯紝鍐嶄粠鍙ｈ嬩腑闅忔満鍙栧嚭涓涓鐞冩槸绾㈢悆鐨勬傜巼涓 锛屾眰鍙ｈ嬩腑鍘熸湁绾㈢悆鍜岄粍鐞冨悇澶氬皯涓.
22锛庯紙10鍒嗭級涓轰簡娴嬮噺涓绉嶅渾褰㈤浂浠剁殑绮惧害锛屽湪鍔犲伐娴佹按绾夸笂璁捐′簡鐢ㄤ袱鍧楀ぇ灏忕浉鍚岋紝涓斿惈鏈30掳瑙掔殑鐩磋掍笁瑙掑昂鎸夌ず鎰忓浘鐨勬柟寮忔祴閲.
锛1锛夎嫢鈯橭鍒嗗埆涓嶢E銆丄F鐩稿垏浜庣偣B銆丆锛
鍏朵腑DA銆丟A杈瑰湪鍚屼竴鐩寸嚎涓.姹傝瘉锛
OA鈯DG锛
锛2锛夊湪锛1锛夌殑鎯呭喌涓嬶紝鑻AC= AF锛屼笖
AF=3锛屾眰寮BC鐨勯暱.
23锛庯紙12鍒嗭級濡傚浘锛屾姏鐗╃嚎y=-x2+bx+c涓巟杞寸殑涓涓浜ょ偣鏄疉锛屼笌y杞寸殑浜ょ偣鏄疊锛屼笖OA銆丱B锛圤A<OB锛夌殑闀挎槸鏂圭▼x2-6x+5=0鐨勪袱涓瀹炴暟鏍.
锛1锛夋眰A銆丅涓ょ偣鐨勫潗鏍囷紱
锛2锛夋眰鍑烘ゆ姏鐗╃嚎鐨勮В鏋愬紡鍙婇《鐐笵鐨勫潗鏍囷紱
锛3锛夋眰鍑烘ゆ姏鐗╃嚎涓巟杞寸殑鍙︿竴涓浜ょ偣C鐨勫潗鏍囷紱
锛4锛夊湪鐩寸嚎BC涓婃槸鍚﹀瓨鍦ㄤ竴鐐筆锛屼娇鍥涜竟褰PDCO涓烘褰锛熻嫢瀛樺湪锛屾眰鍑篜鐐圭殑鍧愭爣锛涜嫢涓嶅瓨鍦锛岃存槑鐞嗙敱.
24锛庯紙12鍒嗭級濡傚浘锛屽湪鐩磋掑潗鏍囩郴xoy涓锛岀偣A锛2锛0锛夛紝鐐笲鍦ㄧ涓璞￠檺涓斺柍OAB涓虹瓑杈逛笁瑙掑舰锛屸柍OAB鐨勫栨帴鍦嗕氦y杞寸殑姝ｅ崐杞翠簬鐐笴锛岃繃鐐笴鐨勫渾鐨勫垏绾夸氦x杞翠簬鐐笵.
锛1锛夊垽鏂鐐笴鏄鍚︿负寮OB鐨勪腑鐐癸紵骞惰存槑鐞嗙敱锛
锛2锛夋眰B銆丆涓ょ偣鐨勫潗鏍囷紱
锛3锛夋眰鐩寸嚎CD鐨勫嚱鏁拌В鏋愬紡锛
锛4锛夌偣P鍦ㄧ嚎娈礝B涓婏紝涓旀弧瓒冲洓杈瑰舰OPCD鏄绛
鑵版褰锛屾眰鐐筆鐨勫潗鏍.
鍙傝冪瓟妗堬細
涓銆侀夋嫨棰橈細BADCB锛 BBCCB.
浜屻佸～绌洪橈細
11锛0.17锛 12锛1<d<3锛 13. a= 鎴0锛
14. 2 锛 15. 锛 16. 3 .
涓夈佽В绛旈橈細
17. 瑙ｏ細鍘熷紡=1-锛2-1锛+2 =1-1+2 +2- = +2.
18. 瑙ｏ細x2-6x+9=锛5-2x锛2锛岋紙x-3锛2=锛5-2x锛2锛
[锛坸-3锛+锛5-2x锛塢[锛坸-3锛-锛5-2x锛塢=0
鈭磝1=2锛寈2= .
19锛庤В锛氬師寮=锛 锛夛紙a+1锛=
= 锛
鐢辨柟绋2x2-x-3=0寰楋細x1= 锛寈2=-1锛
浣嗗綋a=x2=-1鏃讹紝鍒嗗紡鏃犳剰涔夛紱褰揳=x1= 鏃讹紝鍘熷紡=2.
20锛庣暐.
21锛庯紙1锛夌敱棰樻剰寰楋細 锛屾暣鐞嗗緱锛歽= 锛
锛2锛夌敱棰樻剰寰楋細 锛岃В寰楋細x=12锛寉=9锛岀瓟锛氱暐.
22锛庤В锛氾紙1锛夎瘉鏄庯細杩炵粨OB锛孫C锛屸埖AE銆丄F涓衡姍O鐨勫垏绾匡紝BC涓哄垏鐐癸紝
鈭粹垹OBA=鈭燨CA=90掳锛屾槗璇佲垹BAO=鈭燙AO锛
鍙堚垹EAD=鈭燜AG锛屸埓鈭燚AO=鈭燝AO锛
鍙堚垹DAG=180掳锛屸埓鈭燚AO=90掳锛屸埓OA鈯DG.
锛2锛夊洜鈭燨CA=鈭燨BA=90掳锛屼笖鈭燛AD=鈭燜AG=30掳锛屽垯鈭燘AC=120掳锛
鍙圓C= AF=1锛屸垹OAC=60掳锛屾晠OC= 锛屽姬BC鐨勯暱涓 .
23锛庤В锛氾紙1锛夆埖x2-6x+5=0鐨勪袱涓瀹炴暟鏍逛负OA銆丱B锛圤A<OB锛夌殑闀匡紝
鈭碠A=1锛孫B=5锛屸埓A锛1锛0锛夛紝B锛0锛5锛.
锛2锛 鈭垫姏鐗╃嚎y=-x2+bx+c涓巟杞寸殑涓涓浜ょ偣鏄疉锛屼笌y杞寸殑浜ょ偣 B锛
鈭 锛岃В寰楋細 锛
鈭存墍姹備簩娆″嚱鏁扮殑瑙ｆ瀽寮忎负锛歽=-x2-4x+5锛
椤剁偣鍧愭爣涓猴細D锛-2锛9锛.
锛3锛夋ゆ姏鐗╃嚎涓巟杞寸殑鍙︿竴涓浜ょ偣C鐨勫潗鏍囷紙-5锛0锛.
锛4锛夌洿绾緾D鐨勮В鏋愬紡涓猴細y=3x+15锛
鐩寸嚎BC鐨勮В鏋愬紡涓猴細y=x+5锛
鈶犺嫢浠CD涓哄簳锛屽垯OP鈭CD锛岀洿绾縊P鐨勮В鏋愬紡涓猴細y=3x锛
浜庢槸鏈 锛
瑙ｅ緱锛 锛
鈭寸偣P鐨勫潗鏍囦负锛5/2锛15/2锛.
鈶¤嫢浠OC涓哄簳锛屽垯DP鈭CO锛
鐩寸嚎DP鐨勮В鏋愬紡涓猴細y=9锛
浜庢槸鏈 锛
瑙ｅ緱锛 锛
鈭寸偣P鐨勫潗鏍囦负锛4锛9锛夛紝
鈭村湪鐩寸嚎BC涓婂瓨鍦ㄧ偣P锛
浣垮洓杈瑰舰PDCO涓烘褰锛
涓擯鐐圭殑鍧愭爣涓猴紙5/2锛15/2锛夋垨锛4锛9锛.
24锛庤В锛氾紙1锛塁涓哄姬OB鐨勪腑鐐癸紝杩炵粨AC锛
鈭礝C鈯OA锛屸埓AC涓哄渾鐨勭洿寰勶紝
鈭粹垹ABC=90掳锛
鈭碘柍OAB涓虹瓑杈逛笁瑙掑舰锛
鈭粹垹ABO=鈭燗OB=鈭燘AO=60掳锛
鈭碘垹ACB=鈭燗OB=60掳锛
鈭粹垹COB=鈭燨BC=30掳锛
鈭村姬OC=寮BC锛
鍗矯涓哄姬OB鐨勪腑鐐.
锛2锛夎繃鐐笲浣淏E鈯OA浜庣偣E锛屸埖A锛2锛0锛夛紝鈭碠A=2锛孫E=1锛孊E= 锛
鈭寸偣B鐨勫潗鏍囦负锛1锛 锛夛紱
鈭礐涓哄姬OB鐨勪腑鐐癸紝CD鏄鍦嗙殑鍒囩嚎锛孉C涓哄渾鐨勭洿寰勶紝
鈭碅C鈯CD锛孉C鈯OB锛屸埓鈭燙AO=鈭燨CD=30掳锛
鈭碠C= 锛屸埓C锛0锛 锛.
锛3锛夊湪鈻矯OD涓锛屸垹COD=90掳锛孫C= 锛
鈭碠D= 锛屸埓D锛 锛0锛夛紝鈭寸洿绾緾D鐨勮В鏋愬紡涓猴細y= x+ .
锛4锛夆埖鍥涜竟褰OPCD鏄绛夎叞姊褰锛
鈭粹垹CDO=鈭燚CP=60掳锛
鈭粹垹OCP=鈭燙OB=30掳锛屸埓PC=PO.
杩囩偣P浣淧F鈯OC浜嶧锛
鍒橭F= OC= 锛屸埓PF=
鈭寸偣P鐨勫潗鏍囦负:锛 , 锛.