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1銆侀伕瑭炲～绌烘妧宸�

瑭炶獮鐨勯仼鐢ㄥ皪璞�/鎸囦唬鑼冨湇锛氬垎娓呰瑾炵殑涓昏獮鍜岃硴瑾�銆�

瑭炵京鐨勮紩閲嶇▼搴︼細

琛伴€€銆佽“?銆�?ldquo;閫€”鏄笡寮�锛�“鏁�”鏄牬鏁�銆傚悗鑰呴’鐒惰獮缇╄純閲�銆�

閬曞弽銆侀仌鐘細“鍙�”鎸囨柟鍚戠浉鑳�锛�“鐘�”鏄姷瑙搞€�“閬曠姱”姣�“閬曞弽”瑭炵京閲�銆�

瑭炵京鐨勫伌(c猫)閲嶉粸锛�

渚佃ゲ銆佷镜铦曪細瑗�锛岃ゲ鎿�;铦曪紝鎼嶈€�銆�“渚佃ゲ”鎸囦镜鍏ュ苟瑗叉搳鐨勮鐐猴紝鑰�“渚佃潟”鎸囦镜瀹冲苟浣夸箣鍙楁悕銆傚垎鍒ュ伌(c猫)閲嶉亷绋嬪拰绲�(ji茅)鏋�銆�

绶婄己銆佺穵淇忥細缂�锛岀己涔�;淇�锛屾寚璨ㄧ墿鐨勯姺璺ソ銆�“绶婄己”鎸囪波鐗┿€佽硣閲戞垨浜哄摗鍥犵煭缂鸿€岀穵寮�锛�“绶婁繌”鎸囧晢鍝佸洜閵疯矾濂借€屼緵涓嶆噳姹傘€備簩瑭炲悇鍋�(c猫)閲嶄笉鍚岀殑瑙掑害銆�

鑹插僵鎰忕京瀹氶ⅷ鏍硷細

瑜掔京瑭�(鎴愭灉)锛氳偗瀹�銆佸枩鎰� 鍙ｉ牠瑾�(灏忔埃/鑰佸)锛氶€氫織 鑷劧

璨剁京瑭�(鍚庢灉)锛氬惁瀹氥€佸幁妫� 鏇搁潰瑾�(鍚濆棁/绐犺嚰)锛氭枃闆� 鑾婇噸

涓€ц(绲�(ji茅)鏋�)锛氫腑绔�銆佸瑙€

瑾為珨鐗瑰緛鍋氭帓闄わ細

鍏枃閫氬牨锛氭簴纰虹啊鏄�銆佹泛椤槗鎳�锛屾嫆绲曚慨杈寲琛ㄩ仈銆�

鏀胯珫鏅傝⿻锛氶倧杓毚瀵�銆佸畼鏂圭敤瑾�锛岄仼鐣跺舰璞″寲琛ㄩ仈銆�

鏂拌仦鍫遍亾锛氬瑙€绮剧厜銆侀€氫織鏅傛晥锛屼腑鎬ц閬嬬敤杓冨銆�

绉戞妧瑾槑锛氬琛�(sh霉)灏堟キ(y猫)銆佸瑙€鍒嗘瀽锛屼慨杈墜娉曚笉澶氳銆�

鏂囪棟浣滆⿻锛氳獮瑷€钘濊(sh霉)銆佽〃閬旈潏娲伙紝淇经鎵嬫硶杓冨父瑕�銆�

寤ｅ憡瀹ｅ偝锛氬毚璎�?sh霉)鐨縲銆侀啋鐩敓鍕曪紝淇经閬嬬敤杓冭瑳绌�銆�

2銆佺墖娈甸柋璁€鎶€宸�

绲�(ji茅)鍚堥伕闋呭仛鎺掗櫎

灏囬灏惧彞鐨勭閬歌寖鍦嶇敱鍥涘彞绺皬鍒板叐鍙�锛岄渶瑕佺祼(ji茅)鍚堥鍙ラ仼鐢ㄥ師鍓�

A. 鈶も憽鈶犫懃鈶⑩懀 B. 鈶ｂ憽鈶犫懃鈶も憿

C. 鈶♀懃鈶犫懀鈶⑩懁 D. 鈶モ懁鈶♀憿鈶ｂ憼

棣栧熬鍙ユ矑鏈夎(gu墨)寰嬶紝闇€瑕侀€愪竴鎺掓煡锛屽悓鏅傜祼(ji茅)鍚堝収(n猫i)閮ㄩ倧杓拰闂�(gu膩n)绯�

棣栧熬鍏�(n猫i)瀹规湁璎涚┒

棣栧彞涓嶅嚭鐝�(xi脿n)閫欎簺鍏�(n猫i)瀹癸細

鍙嶉潰璜栬瓑锛氬惁鍓�銆佷笉鐒�銆佸鏋滄矑鏈�锛屽鏋滀笉

瑁滃厖琛ㄨ堪锛氱暥鐒躲€佷篃銆佸張

鎸囩ず浠ｈ锛氶€�銆侀€欎簺銆侀偅銆侀偅浜�銆佹

绲�(ji茅)璜栫附绲�(ji茅)锛氬洜姝ゃ€佹墍浠�銆佹渶绲�銆佺祩浜�

棣栧彞鍙互鍑虹従(xi脿n)閫欎簺鍏�(n猫i)瀹癸細

寮曠敤鐨勫垾浜虹殑瑙€榛� 鑳屾櫙鎬х殑闄宠堪 瑷晱鎻愬嚭瑭遍

灏惧彞涓€鑸嚭鐝�(xi脿n)閫欎簺鍏�(n猫i)瀹癸細

鍥犳銆佸洜鑰�銆佺附涔嬨€佸彲瑕�銆佺稖涓婃墍杩�

鏁�(sh霉)閲忛棞(gu膩n)绯�

1.浠ｅ叆鎺掗櫎锛�

浠ｅ叆鎺掗櫎鎬濈董鏄暩(sh霉)閲忛棞(gu膩n)绯荤涓€澶ф硶锛屽劒(y艒u)鍏堣€冩叜銆�

2.鐗瑰€兼€濈董锛�

灏嶄簬鏈変簺鍟忛锛岃嫢鑳芥牴鎿�(j霉)鍏跺叿楂旀儏娉�锛屽悎鐞嗗阀濡欏湴灏嶆煇浜涘厓绱犺肠鍊�锛岀壒鍒ユ槸璩︿簣纰哄畾鐨勭壒娈婂€�锛屽線寰€鑳戒娇鍟忛鐛插緱绨℃嵎鏈夋晥鐨勮В姹�銆傞骞蹭腑鏈夊垎鏁�(sh霉)锛屾瘮渚�锛屾垨鑰呭€嶆暩(sh霉)闂�(gu膩n)绯绘檪涓€鑸噰鐢ㄨ肠鍊兼硶绨″寲瑷堢畻锛岃肠鍊兼硶缍�(j墨ng)甯告噳鐢ㄥ湪濡傚伐绋嬪晱椤岋紝琛岀▼鍟忛锛岃不鐢ㄥ晱椤岀瓑椤岀洰涓�銆�

3.鍊嶆暩(sh霉)姣斾緥娉曪細

鑻 : b=m : n(m銆乶浜掕唱(zh矛))锛�

鍓囪鏄�: a鍗爉浠�锛屾槸m鐨勫€嶆暩(sh霉);

b鍗爊浠�锛屾槸n鐨勫€嶆暩(sh霉);

a+b鍗爉+n浠�锛屾槸m+n鐨勫€嶆暩(sh霉);

a-b鍗爉-n浠斤紝鏄痬-n鐨勫€嶆暩(sh霉)銆�

4.濂囧伓鐗规€ф硶锛�

鍏╁€嬪鏁�(sh霉)涔嬪拰/宸偤鍋舵暩(sh霉)锛屽叐鍊嬪伓鏁�(sh霉)涔嬪拰/宸偤鍋舵暩(sh霉)锛屼竴濂囦竴鍋朵箣鍜�/宸偤濂囨暩(sh霉);

鍏╁€嬫暩(sh霉)鐨勫拰宸偤濂囨暩(sh霉)锛屽墖瀹冨€戝鍋剁浉鍙�锛屽叐鍊嬫暩(sh霉)鐨勫拰/宸偤鍋舵暩(sh霉)锛屽墖瀹冨€戝鍋剁浉鍚�;

鍏╁€嬫暩(sh霉)鐨勫拰鐐哄鏁�(sh霉)锛屽墖鍏跺樊涔熺偤濂囨暩(sh霉)锛屽叐鍊嬫暩(sh霉)鐨勫拰鐐哄伓鏁�(sh霉)锛屽墖鍏跺樊涔熺偤鍋舵暩(sh霉)

5.鏂圭▼娉曪細

寰堝鏁�(sh霉)瀛搁亱绠楅鐩兘鍙互閲囩敤鍒楁柟绋嬮€茶姹傝В銆�

鏂圭▼娉曟敞鎰忎簨闋咃細鏈煡鏁�(sh霉)瑕佷究浜庡垪鏂圭▼;鏈煡鏁�(sh霉)鍙互鐢ㄥ瓧姣嶈〃绀�锛屼篃鍙互鐢�“浠芥暩(sh霉)”锛岄倓鍙互鐢ㄦ饥瀛楅€茶鏇夸唬銆�

浜斿ぇ妯″瀷

妯″瀷涓€锛氱墰鍚冭崏妯″瀷

姝ゆā鍨嬫槸鎸囧瓨鍦ㄤ竴鍊嬪畾閲�锛屽悓鏅傛棦鏈変娇鍏跺鍔犵殑閲忥紝涔熸湁浣垮叾娓涘皯鐨勯噺锛岀啊鍠鎷氨鏄湁閫叉湁鍑恒€傞€欑ó椤屽瀷甯歌鐨勫氨鏄互鎺掓瘮鍙ョ殑褰㈠紡鍑虹従(xi脿n)锛屽苟涓旀瘡涓€鍙ヨ┍涓兘鏈冨嚭鐝�(xi脿n)鍏╁€嬫暩(sh霉)锛屼竴鍊嬭〃绀烘暩(sh霉)閲�锛屼竴鍊嬭〃绀烘檪闁�銆�

绀轰緥锛氱墽鍫翠笂鏈変竴鐗囬潚鑽�锛屾瘡澶╅兘鐢熼暦寰椾竴妯ｅ揩銆傞€欑墖闈掕崏渚涚郸N1闋墰鍚冿紝鍙互鍚僼1澶�锛屾垨鑰呬緵绲2闋墰鍚冿紝鍙互鍚僼2澶�锛屽鏋滀緵绲3闋墰鍚�锛屽彲浠ュ悆骞惧ぉ?

灏嶄簬閫欑ó椤屽瀷鏍稿績鍏紡锛氬師鏈夎崏閲�=(N1-X)×t1 =(N2-X)×t2=(N3-X)×t3

鎵€浠ュ彧闇€瑕佹牴鎿�(j霉)椤屽共鐨勮(gu墨)寰嬶紝鐢ㄨ〃绀烘暩(sh霉)閲忕殑鏁�(sh霉)瀛�-x鐨勭祼(ji茅)鏋滀箻浠ュ皪鎳夌殑鏅傞枔鍒楀嚭鏂圭▼鍗冲彲銆�

渚嬮 鐗у牬涓婃湁涓€鐗囬潚鑽�锛屾瘡澶╅兘鐢熼暦寰椾竴妯ｅ揩銆傞€欑墖闈掕崏渚涚郸10闋墰鍚�锛屽彲浠ュ悆22澶�锛屾垨鑰呬緵绲�16闋墰鍚冿紝鍙互鍚�10澶�锛屽鏋滀緵绲�27闋墰鍚�锛屽彲浠ュ悆骞惧ぉ?

A銆�5 B銆�6 C銆�7 D銆�8

绛旀锛欰 鍒嗘瀽锛�(10-x)×22=(16-x)×10=(27-x)×t3

瑙ｄ箣寰� X=5,t3=5澶�

甯歌褰㈠紡锛氱墰鍚冭崏銆佹帓闅婃敹閵€/妾㈢エ銆佹娊姘存斁姘�銆侀枊閲囪硣婧愩€佺埇鑷嫊鎵舵绛�銆�

妯″瀷浜岋細鐩寸窔澶氭鐩搁亣鍟忛

寰炲叐鍦板悓鏅傚嚭鐧�(f膩)鐨勭洿绶氱浉閬囧晱椤屼腑锛岀n娆＄浉閬囨檪锛岃矾绋嬪拰绛変簬绗竴娆＄浉閬囨檪璺▼鍜岀殑2n-1鍊�锛屾瘡鍊嬩汉璧扮殑璺▼绛変簬浠栫涓€娆＄浉閬囨檪鎵€璧拌矾绋嬬殑2n-1鍊�銆�

妯″瀷涓夛細閷綅閲嶆帓鍟忛

姣忎竴灏嶅厓绱犻兘鏈変竴鍊嬩竴涓€灏嶆噳闂�(gu膩n)绯�锛屽晱鎵撶牬姣忎竴灏嶄竴涓€灏嶆噳闂�(gu膩n)绯荤殑鏂规硶鏁�(sh霉)锛屾绋柟娉曞彨鍋氶尟浣嶉噸鎺掋€�

妯″瀷鍥涳細鐠�(hu谩n)褰㈡帓鍒�

妯″瀷浜旓細澶氭鐛ㄧ珛閲嶅京瑭﹂

鍒ゆ柗鎺ㄧ悊

鍦栧舰鎺ㄧ悊瑕�(gu墨)寰�

1.鍏冪礌鍑屼簜锛氶骞蹭腑鍚勫湒褰㈠厓绱犲噷浜�锛屽咕涔庢矑鏈夌浉鍚岄粸锛屽劒(y艒u)鍏堣€冩叜鏁�(sh霉)閲忛棞(gu膩n)绯荤殑鑰冮粸锛岃(gu墨)寰嬬殑鍑虹櫦(f膩)榛炲彲浠ユ槸锛氶粸銆佺窔銆佽銆侀潰銆佺礌銆傚厓绱犲噷浜傞櫎浜嗚€冩煡鍦栧舰鐨勬暩(sh霉)閲忛棞(gu膩n)绯诲锛岄倓鍙兘鑰冪殑鏄湒褰㈢殑灞€э紝鍗冲咕浣曠壒寰�銆�

2.鍏冪礌鐩稿悓銆傞骞插湒褰腑鎵€鍖呭惈鐨勫厓绱犲€嬫暩(sh霉)鑸囩ó椤炵浉鍚岋紝鍎�(y艒u)鍏堣€冩叜鍦栧舰鐨勪綅缃畩鍖�锛屽寘鎷湒褰腑鍏冪礌鐨勫钩绉�銆佹棆杞�(zhu菐n)浠ュ強缈昏綁(zhu菐n)銆�

3.鍏冪礌鐩镐技銆傞骞插悇鍦栧舰鍏冪礌鍛堢従(xi脿n)鐩镐技鐨勭壒寰�锛屽湪鍏冪礌鍊嬫暩(sh霉)涓婂彲鑳藉瓨鍦ㄥ樊鐣帮紝鍓囧彲浠ヨ€冩叜鍦栧舰鐨勬ǎ寮忛亶姝�(缂轰粈涔堣浠€涔�)銆佺祫鍚堢枈鍔�(鐩存帴鐤婂姞銆佸姞娓涘悓鐣�銆侀粦鐧界枈鍔�)銆�

4.绌洪枔鎶樼枈銆傜┖闁撴姌鐤婇鏈€閲嶈鐨勬槸鍒嗘瀽鍦栧舰鐨勭浉閯伴潰鍜岀浉灏嶉潰锛屽彲浠ラ€氶亷绉诲嫊鐨勬柟寮忔壘婧栧悇闈箣闁撶殑闂�(gu膩n)绯�锛屾牴鎿�(j霉)“鐩稿皪闈㈠彧鑳界湅鍒板叾涓竴鍊�銆佺浉閯伴潰鐪嬪叕鍏遍倞”鐨勭壒寰侀伕鎿囨纰虹瓟妗�

鍒ゆ柗鎺ㄧ悊瑕�(gu墨)寰�

缈昏鎺ㄧ悊

涓夊€嬪熀鏈畾鐞�

閫嗗惁瀹氱悊锛欰鎺ㄥ嚭B→鍚鎺ㄥ嚭鍚

鑲墠鑲悗锛屽惁鍚庡惁鍓�

鎽╂牴瀹氬緥1锛氬惁(A鎴朆)→鍚涓斿惁B

鎽╂牴瀹氬緥2锛氬惁(A涓擝)→鍚鎴栧惁B

涓冩鍩烘湰缈昏

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娌掓湁S鏄疨锛宲鎺ㄥ嚭闈濻

涓嶆槸S閮戒笉鏄疨锛孭鎺ㄥ嚭S

鍏呭垎姊濅欢锛歅鎺ㄥ嚭Q銆傚鏋淧锛岄偅涔圦;鍙P锛屽氨Q;鍑℃槸P锛岄兘Q

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鎺掍腑寰嬶細闈濸鍗砆锛岄潪Q鍗砅?锛涜洏閫�锛屾垨鑰匭;瑕佷箞P锛岃涔圦

涓夌ó鍩烘湰闂�(gu膩n)绯�

鐭涚浘闂�(gu膩n)绯�

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鍖呭闂�(gu膩n)绯�

鍖呭鏄寚锛岃嫢A鐪�锛屽墖B涔熺湡锛屽嵆鏈夛細A→B銆傚叐鍊嬪懡椤�锛岃嫢鍛介涓彧鏈変竴鐪�锛屽墖A蹇呯偤鍋�;鑻ュ懡椤屼腑鍙湁涓€鍋囷紝鍓嘊蹇呯偤鐪�銆�“涓€鐪熷墠鍋�锛屼竴鍋囧悗鐪�”

閭忚集璜栬瓑

1. 鍔犲挤璜栬瓑

(1)闈炲洜鏋滈锛�

鈶犲寮疯珫榛�(閫氶亷瑙ｉ噵銆侀噸鐢宠珫榛為€茶鍔犲挤)

鈶″寮疯珫鎿�(j霉)锛氬垎鐐哄叐绋紝涓€绋槸瑁滃厖涓€鍊嬫闈㈣珫鎿�(j霉)锛屽彟涓€绋槸瑙ｉ噵鍘熸湁鐨勮珫鎿�(j霉)锛屼簩鑰呭潎鍙捣鍒板姞寮蜂綔鐢�

鈶㈠緸璜栬瓑鏂瑰紡鍏ユ墜锛氭惌姗�(灏囪珫榛炶垏璜栨摎(j霉)鑱�(li谩n)绯昏捣渚�锛屽線寰€鏃㈠寘鍚珫鎿�(j霉)鐨勯棞(gu膩n)閸佃鍙堝寘鍚珫榛炵殑闂�(gu膩n)閸佃銆�)鍜岃鍏呭墠鎻�(閫欐槸璜栭粸寰椾互鎴愮珛鐨勫繀瑕佹浠�/鍩虹锛屽彲浠ョ敤鍚﹀畾浠ｅ叆娉曢€茶椹楄瓑)銆�

(2)鍥犳灉椤烇細鈶犳帓闄や粬鍥�—鎺掗櫎鍏朵粬灏庤嚧绲�(ji茅)鏋滃嚭鐝�(xi脿n)鐨勫師鍥�;鈶″皪姣斿椹�—鏈堿鏈塀锛屾矑A娌払銆�

鑰冭│閬庣▼涓�锛岀暥鍑虹従(xi脿n)澶氬€嬪姞寮烽伕闋呮檪锛屾敞鎰忓姞寮峰挤搴︾殑姣旇純锛氬姞寮疯珫璀夋柟寮�(鎼⿱)>鍔犲挤璜栭粸>鍔犲挤璜栨摎(j霉)銆傝€屽皪浜庨伕鎿囧墠鎻愮殑椤岀洰渚嗚锛岀洿鎺ュ氨椤岀洰瑷晱鏂瑰紡閬告搰鍓嶆彁銆�

2. 鍓婂急璜栬瓑

(1)闈炲洜鏋滈锛氣憼鍓婂急璜栭粸;鈶″墛寮辫珫鎿�(j霉);鈶㈠墛寮辫珫璀夋柟寮�(鎷嗘⿱);鈶ｅ惁瀹氬墠鎻愩€�

(2)鍥犳灉椤烇細鈶犲彟鏈変粬鍥�—閭勬湁鍏朵粬鍘熷洜?q奴)械闄哬(ji茅)鏋滅殑鍑虹従(xi脿n);鈶″皪姣斿椹�—鏈堿鐒锛岀劇A鏈塀;鈶㈠洜鏋滃€掔疆銆�

鑰冪敓閫氶亷涓婅堪鐨勮娓附绲�(ji茅)锛屽彲浠ュ皣浠ュ線鐨勭煡璀橀粸閫茶绺界祼(ji茅)鍜屾⒊鐞�锛岀湅鍝竴鍊嬬挵(hu谩n)绡€(ji茅)閭勬矑鏈夊緢濂界殑鎺屾彙锛屽彲浠ラ€茶鏌ユ紡瑁滅己銆傛洿澶氶棞(gu膩n)浜庣殑鑰冭│淇℃伅鑰冪敓閫氶亷 鍏嶈不闋愮磩鐭俊鎻愰啋鏈嶅嫏锛岀挵(hu谩n)鐞冪恫(w菐ng)鏍℃渻绲﹁€冪敓浠ョ煭淇＄殑褰㈠紡鐧�(f膩)閫佽€冭│鐨勬檪闁撳拰娉ㄦ剰浜嬮爡锛屾洿澶氭妧宸ф€х殑鍌欒€冭硣鏂�锛岃€冪敓鍙互榛炴搳涓嬫柟閺堟帴鍏嶈不闋樺彇渚嗙獊鎿婅嚜宸辩殑鍒嗘暩(sh霉)銆�