目錄初一數(shù)學(xué)下冊重點筆記 初一數(shù)學(xué)易錯題100道 初一數(shù)學(xué)必考知識點總結(jié) 初一數(shù)學(xué)重點知識歸納 數(shù)學(xué)初一知識點總結(jié)歸納
鍒濅竴鏁板?︾煡璇嗙偣濡備笅錛?
1銆佹暟杞寸殑涓夌墿铏氬崌瑕佺礌錛氬師鐐廣?佹?ｆ柟鍚戙?佸崟浣嶉暱搴︺??
2銆佺粷瀵瑰?鹼細緇濆?瑰?兼槸鎸囦竴涓?鏁板湪鏁拌醬涓婃墍瀵瑰簲鐐瑰埌鍘熺偣鐨勮窛紱匯?傛?ｆ暟鐨勭粷瀵瑰?兼槸瀹冪僵鑰佹湰韜?錛岃礋鏁扮殑緇濆?瑰?兼槸瀹冪殑鐩稿弽鏁?;0鐨勭粷瀵瑰?兼槸0錛屼袱涓?璐熸暟錛岀粷瀵瑰?煎ぇ鐨勫弽鑰屽皬銆?
3銆佸姞娉曚氦鎹㈠緥錛歛+b= b+ a 涓や釜鏁扮浉鍔狅紝浜ゆ崲鍔犳暟鐨勪綅緗?錛屽拰涓嶅彉銆?
4銆佽礋鏁扮殑濂囨暟嬈″箓鏄?璐熸暟錛岃礋鏁扮殑鍋舵?″箓鏄?姝ｆ暟錛?0鐨勪換浣曟?ｈ獕縐熸暣鏁版?″箓閮芥槸0銆?
5銆佸?氶」寮忥細鍑犱釜鍗曢」寮忕殑鍜屽彨鍋氬?氶」寮忋??
鍒濅竴鏁板?︾殑涓昏?佺煡璇嗙偣閮芥湁鍝?浜?
鍒濅竴鏁板?︿富瑕佺煡璇嗙偣:
浠ｆ暟鍒濇?ョ煡璇?
1. 浠ｆ暟寮?:鐢ㄨ繍綆楃?﹀彿鈥?+ - 脳 梅 鈥︹?? 鈥濊繛鎺ユ暟鍙婅〃紺烘暟鐨勫瓧姣嶇殑寮忓瓙縐頒負浠ｆ暟寮?.娉ㄦ剰:鐢ㄥ瓧姣嶈〃紺烘暟鏈変竴瀹氱殑闄愬埗,棣栧厛瀛楁瘝鎵?鍙栧緱鏁板簲淇濊瘉瀹冩墍鍦ㄧ殑寮忓瓙鏈夋剰涔?,鍏舵?″瓧姣嶆墍鍙栧緱鏁拌繕搴斾嬌瀹為檯鐢熸椿鎴栫敓浜ф湁鎰忎箟;鍗曠嫭涓?涓?鏁版垨涓?涓?瀛楁瘝涔熸槸浠ｆ暟寮忋??
2. 鍑犱釜閲嶈?佺殑浠ｆ暟寮?:(m銆乶琛ㄧず鏁存暟)
(1)a涓巄鐨勫鉤鏂瑰樊鏄?: a2-b2 ; a涓巄宸?鐨勫鉤鏂規(guī)槸:(a-b)2 ;
(2)鑻?a銆乥銆乧鏄?姝ｆ暣鏁?,鍒欎袱浣嶆暣鏁版槸: 10a+b ,鍒欎笁浣嶆暣鏁版槸:100a+10b+c;
(3)鑻?m銆乶鏄?鏁存暟,鍒欒??5闄ゅ晢m浣檔鐨勬暟鏄?: 5m+n ;鍋舵暟鏄?:2n ,濂囨暟鏄?:2n+1;涓変釜榪炵畫鏁存暟鏄?: n-1銆乶銆乶+1 ;
(4)鑻?b>0,鍒欐?ｆ暟鏄?:a2+b ,璐熸暟鏄?: -a2-b ,闈炶礋鏁版槸: a2 ,闈炴?ｆ暟鏄?:-a2 .
鏈夌悊鏁?
鍑¤兘鍐欐垚q/p(p,q涓烘暣鏁頒笖p鈮?0)褰㈠紡鐨勬暟,閮芥槸鏈夌悊鏁?.姝ｆ暣鏁般??0銆佽礋鏁存暟緇熺О鏁存暟;姝ｅ垎鏁般?佽礋鍒嗘暟緇熺О鍒嗘暟;鏁存暟鍜屽垎鏁扮粺縐版湁鐞嗘暟.娉ㄦ剰:0鏃?涓嶆槸姝ｆ暟,涔熶笉鏄?璐熸暟;-a涓嶄竴瀹氭槸璐熸暟,+a涔熶笉涓?瀹氭槸姝ｆ暟;p涓嶆槸鏈夌悊鏁?;
鏈夌悊鏁板姞娉曟硶鍒?:
(1)鍚屽彿涓ゆ暟鐩稿姞,鍙栫浉鍚岀殑絎﹀彿,騫舵妸緇濆?瑰?肩浉鍔?;
(2)寮傚彿涓ゆ暟鐩稿姞,鍙栫粷瀵瑰?艱緝澶х殑絎﹀彿,騫剁敤杈冨ぇ鐨勭粷瀵瑰?煎噺鍘昏緝?yōu)畯鐨劸l濆?瑰??;
(3)涓?涓?鏁頒笌0鐩稿姞,浠嶅緱榪欎釜鏁?.
鏈夌悊鏁板姞娉曠殑榪愮畻寰?:
(1)鍔犳硶鐨勪氦鎹㈠緥:a+b=b+a ;(2)鍔犳硶鐨勭粨鍚堝緥:(a+b)+c=a+(b+c).
鏈夌悊鏁板噺娉曟硶鍒?:鍑忓幓涓?涓?鏁?,絳変簬鍔犱笂榪欎釜鏁扮殑鐩稿弽鏁?;鍗砤-b=a+(-b).
鏈夌悊鏁頒箻娉曟硶鍒?:
(1)涓ゆ暟鐩鎬箻,鍚屽彿涓烘??,寮傚彿涓鴻礋,騫舵妸緇濆?瑰?肩浉涔?;
(2)浠諱綍鏁板悓闆剁浉涔橀兘寰楅浂;
(3)鍑犱釜鏁扮浉涔?,鏈変竴涓?鍥犲紡涓洪浂,縐?涓洪浂;鍚勪釜鍥犲紡閮戒笉涓洪浂,縐?鐨勭?﹀彿鐢辮礋鍥犲紡鐨勪釜鏁板喅瀹?.
鏈夌悊鏁頒箻娉曠殑榪愮畻寰?:
(1)涔樻硶鐨勪氦鎹㈠緥:ab=ba;(2)涔樻硶鐨勭粨鍚堝緥:(ab)c=a(bc);
(3)涔樻硶鐨勫垎閰嶅緥:a(b+c)=ab+ac .
鏈夌悊鏁伴櫎娉曟硶鍒?:闄ょ氦澶ц～浠ヤ竴涓?鏁扮瓑浜庝箻浠ヨ繖涓?鏁扮殑鍊掓暟;娉ㄦ剰:闆朵笉鑳藉仛闄ゆ暟銆?
鏁村紡鐨勫姞鍑?
鍗曢」寮?:鍦ㄤ唬鏁板紡涓?,鑻ュ彧鍚?鏈変箻娉?(鍖呮嫭涔樻柟)榪愮畻銆傛垨铏藉惈鏈夐櫎娉曡繍綆?,浣嗛櫎寮忎腑涓嶅惈瀛楁瘝鐨勪竴綾諱唬鏁板紡鍙?鍗曟瘉鑵旈」寮?.
鍗曢」寮忕殑`緋繪暟涓庢?℃暟:鍗曢」寮忎腑涓嶄負闆剁殑鏁板瓧鍥犳暟,鍙?鍗曢」寮忕殑鏁板瓧緋繪暟,綆?縐板崟欏瑰紡鐨勭郴鏁?;緋繪暟涓嶄負闆舵椂,鍗曢」寮忎腑鎵?鏈夊瓧姣嶆寚鏁扮殑鍜?,鍙?鍗曢」寮忕殑嬈℃暟.
澶氶」寮?:鍑犱釜鍗曢」寮忕殑鍜屽彨澶氶」寮?.
澶氶」寮忕殑欏規(guī)暟涓庢?℃暟:澶氶」寮忎腑鎵?鍚?鍗曢」寮忕殑涓?鏁板氨鏄?澶氶」寮忕殑欏規(guī)暟,姣忎釜鍗曢」寮忓彨澶氶」寮忕殑欏?;澶氶」寮忛噷,嬈℃暟欏圭殑嬈℃暟鍙?澶氶」寮忕殑嬈℃暟;娉ㄦ剰:(鑻?a銆乥銆乧銆乸銆乹鏄?甯告暟)ax2+bx+c鍜寈2+px+q鏄?甯歌?佺殑涓や釜浜屾?′笁欏瑰紡.
鏁村紡:鍑′笉鍚?鏈夐櫎娉曡繍綆?,鎴栬櫧鍚?鏈夐櫎娉曡繍綆椾絾闄ゅ紡涓?涓嶅惈瀛楁瘝鐨勪唬鏁板紡鍙?鏁村紡.
涓?鍏冧竴嬈℃柟紼?
涓?鍏冧竴嬈℃柟紼?:鍙?鍚?鏈変竴涓?鏈?鐭ユ暟,騫朵笖鏈?鐭ユ暟鐨勬?℃暟鏄?1,騫朵笖鍚?鏈?鐭ユ暟欏圭殑緋繪暟涓嶆槸闆剁殑鏁村紡鏂圭▼鏄?涓?鍏冧竴嬈℃柟紼?.
涓?鍏冧竴嬈℃柟紼嬬殑鏍囧噯褰㈠紡: ax+b=0(x鏄?鏈?鐭ユ暟,a銆乥鏄?宸茬煡鏁?,涓攁鈮?0).
涓?鍏冧竴嬈℃柟紼嬬殑鏈?綆?褰㈠紡: ax=b(x鏄?鏈?鐭ユ暟,a銆乥鏄?宸茬煡鏁?,涓攁鈮?0).
涓?鍏冧竴嬈℃柟紼嬭В娉曠殑涓?鑸?姝ラ??: 鏁寸悊鏂圭▼ 鈥︹?? 鍘誨垎姣? 鈥︹?? 鍘繪嫭鍙? 鈥︹?? 縐婚」 鈥︹?? 鍚堝茍鍚岀被欏? 鈥︹?? 緋繪暟鍖栦負1 鈥︹?? (媯?楠屾柟紼嬬殑瑙?).
鍒楁柟紼嬭В搴旂敤棰樼殑甯哥敤鍏?寮?:
(1)琛岀▼闂?棰?:璺濈??=閫熷害路鏃墮棿;
(2)宸ョ▼闂?棰?:宸ヤ綔閲?=宸ユ晥路宸ユ椂;
(3)姣旂巼闂?棰?:閮ㄥ垎=鍏ㄤ綋路姣旂巼;
(4)欏洪?嗘祦闂?棰?:欏烘祦閫熷害=闈欐按閫熷害+姘存祦閫熷害,閫嗘祦閫熷害=闈欐按閫熷害-姘存祦閫熷害;
(5)鍟嗗搧浠鋒牸闂?棰?:鍞?浠?=瀹氫環(huán)路鎶樎?0.1 ,鍒╂鼎=鍞?浠?-鎴愭湰;
(6)鍛ㄩ暱銆侀潰縐?銆佷綋縐?闂?棰?:C鍦?=2蟺R,S鍦?=蟺R2,C闀挎柟褰?=2(a+b),S闀挎柟褰?浠垮厔=ab, C姝ｆ柟褰?=4a,S姝ｆ柟褰?=a2,S鐜?褰?=蟺(R2-r2),V闀挎柟浣?=abc ,V姝ｆ柟浣?=a3,V鍦嗘煴=蟺R2h ,V鍦嗛敟=1/3蟺R2h.
瀛︿範浠庢潵鏃犳嵎寰勩?傛瘡涓?闂ㄧ?戠洰閮芥湁鑷?宸辯殑瀛︿範 鏂規(guī)硶 錛屼絾鍏跺疄閮芥槸涓囧彉涓嶇?誨叾涓?鐨勶紝鏁板?︿綔涓轟富縐戜箣涓?錛屽拰璇?鏂囪嫳璇?涓?鏍鳳紝涔熸槸瑕佽?般?佽?佽儗銆佽?佽?茬粌鐨勩?備笅闈㈡槸鎴戠粰澶у?舵暣鐞嗙殑涓?浜涘垵涓?鏁板?︾殑鐭ヨ瘑鐐瑰厔鎮(zhèn)斿眬錛屽笇鏈涘?瑰ぇ瀹舵湁鎵?甯?鍔┿??
鍒濅腑涓?騫寸駭鏁板??涓婂唽鐭ヨ瘑鐐?
鍥懼艦鐨勫垵姝ヨ?よ瘑
涓?銆佺珛浣撳浘褰?涓庡鉤闈㈠浘褰?
1銆侀暱鏂逛綋銆佹?ｆ柟浣撱?佺悆銆佸渾鏌便?佸渾閿ョ瓑閮芥槸绔嬩綋鍥懼艦銆傛?ゅ?栨１鏌便?佹１閿ヤ篃鏄?甯歌?佺殑绔嬩綋鍥懼艦銆?
2銆侀暱鏂瑰艦銆佹?ｆ柟褰?銆佷笁瑙掑艦銆佸渾絳夐兘鏄?騫抽潰鍥懼艦銆?
3銆佽?稿?氱珛浣撳浘褰㈡槸鐢變竴浜涚盡璁╁鉤闈㈠浘褰㈠洿鎴愮殑錛屽皢瀹冧滑閫傚綋鍦板壀寮?錛屽氨鍙?浠ュ睍寮?鎴愬鉤闈㈠浘褰?銆?
浜屻?佺偣鍜岀嚎
1銆佺粡榪囦袱鐐規(guī)湁涓?鏉＄洿綰匡紝騫朵笖鍙?鏈変竴鏉＄洿綰褲??
2銆佷袱鐐逛箣闂寸嚎孌墊渶鐭?銆?
3銆佺偣C綰挎?礎(chǔ)B鍒嗘垚鐩哥瓑鐨勪袱鏉″墠紓ㄧ嚎孌礎(chǔ)M涓嶮B錛岀偣M鍙?鍋氱嚎孌礎(chǔ)B鐨勪腑鐐廣?傜被浼肩殑榪樻湁綰挎?電殑涓夌瓑鍒嗙偣銆佸洓絳夊垎鐐圭瓑銆?
4銆佹妸綰挎?靛悜涓?鏂規(guī)棤闄愬歡浼告墍褰㈡垚鐨勫浘褰㈠彨鍋氬皠綰褲??
涓夈?佽??
1銆佽?掓槸鐢變袱鏉℃湁鍏?鍏辯??鐐圭殑灝勭嚎緇勬垚鐨勫浘褰?銆?
2銆佺粫鐫?绔?鐐規(guī)棆杞?鍒拌?掔殑緇堣竟鍜屽?嬭竟鎴愪竴鏉＄洿綰匡紝鎵?鎴愮殑瑙掑彨鍋氬鉤瑙掋??
3銆佺粫鐫?绔?鐐規(guī)棆杞?鍒扮粓杈瑰拰濮嬭竟鍐嶆?￠噸鍚堬紝鎵?鎴愮殑瑙掑彨鍋氬懆瑙掋??
4銆佸害銆佸垎銆佺?掓槸甯哥敤鐨勮?掔殑搴﹂噺鍗曚綅銆?
鎶婁竴涓?鍛ㄨ??360絳夊垎錛屾瘡涓?浠藉氨鏄?涓?搴︾殑瑙掞紝璁頒綔1擄;鎶?1搴︾殑瑙?60絳夊垎錛屾瘡浠藉彨鍋?1鍒嗙殑瑙掞紝璁頒綔1鈥?;鎶?1鍒嗙殑瑙?60絳夊垎錛屾瘡浠藉彨鍋?1縐掔殑瑙掞紝璁頒綔1鈥熾??
鍒濅竴涓嬪唽鏁板?︾煡璇嗙偣
1.璁よ瘑涓夎?掑艦錛屼簡瑙ｄ笁瑙掑艦鐨勬剰涔夛紝璁よ瘑涓夎?掑艦鐨勮竟銆佸唴瑙掋?侀《鐐癸紝鑳界敤絎﹀彿璇?璦?琛ㄧず涓夎?掑艦銆?
2.緇忓巻搴﹂噺涓夎?掑艦杈歸暱鐨勫疄璺墊椿鍔ㄤ腑錛岀悊瑙ｄ笁瑙掑艦涓夎竟涓嶇瓑鐨勫叧緋匯??
3.鎳傚緱鍒ゆ柇涓夋潯綰挎?靛彲鍚︽瀯鎴愪竴涓?涓夎?掑艦鐨勬柟娉曪紝騫惰兘榪愮敤瀹冭В鍐蟲湁鍏崇殑闂?棰樸??
4.涓夎?掑艦鐨勫唴瑙掑拰瀹氱悊錛岃兘鐢ㄥ鉤琛岀嚎鐨勬?ц川鎺ㄥ嚭榪欎竴瀹氱悊銆?
5.鑳藉簲鐢ㄤ笁瑙掑艦鍐呰?掑拰瀹氱悊瑙ｅ喅涓?浜涚畝鍗曠殑瀹為檯闂?棰樸??
浜屻?侀噸鐐?
涓夎?掑艦鍐呰?掑拰瀹氱悊;
瀵逛笁瑙掑艦鏈夊叧姒傚康鐨勪簡瑙ｏ紝鑳界敤絎﹀彿璇?璦?琛ㄧず涓夋潯褰?銆?
涓夈?侀毦鐐?
涓夎?掑艦鍐呰?掑拰瀹氱悊鐨勬帹鐞嗙殑榪囩▼;
鍦ㄥ叿浣撶殑鍥懼艦涓?涓嶉噸澶嶏紝涓斾笉閬楁紡鍦拌瘑鍒?鎵?鏈変笁瑙掑艦;
鐢ㄤ笁瑙掑艦涓夎竟涓嶇瓑鍏崇郴鍒ゅ畾涓夋潯綰挎?靛彲鍚︾粍鎴愪笁瑙掑艦銆?
鍥涖?佺煡璇嗘?嗘灦
浜斻?佺煡璇嗙偣銆佹?傚康鎬葷粨
1.涓夎?掑艦錛氱敱涓嶅湪鍚屼竴鐩寸嚎涓婄殑涓夋潯綰挎?甸?栧熬欏烘?＄浉鎺ユ墍緇勬垚鐨勫浘褰㈠彨鍋氫笁瑙掑艦銆?
2.涓夎?掑艦鐨勫垎綾?
3.涓夎?掑艦鐨勪笁杈瑰叧緋伙細涓夎?掑艦浠繪剰涓よ竟鐨勫拰澶т簬絎?涓夎竟錛屼換鎰忎袱杈圭殑宸?灝忎簬絎?涓夎竟銆?
4.楂橈細浠庝笁瑙掑艦鐨勪竴涓?欏剁偣鍚戝畠鐨勫?硅竟鎵?鍦ㄧ洿綰夸綔鍨傜嚎錛岄《鐐瑰拰鍨傝凍闂寸殑綰挎?靛彨鍋氫笁瑙掑艦鐨勯珮銆?
5.涓?綰匡細鍦ㄤ笁瑙掑艦涓?錛岃繛鎺ヤ竴涓?欏剁偣鍜屽畠鐨勫?硅竟涓?鐐圭殑綰挎?靛彨鍋氫笁瑙掑艦鐨勪腑綰褲??
6.瑙掑鉤鍒嗙嚎錛氫笁瑙掑艦鐨勪竴涓?鍐呰?掔殑騫沖垎綰夸笌榪欎釜瑙掔殑瀵硅竟鐩鎬氦錛岃繖涓?瑙掔殑欏剁偣鍜屼氦鐐逛箣闂寸殑綰挎?靛彨鍋氫笁瑙掑艦鐨勮?掑鉤鍒嗙嚎銆?
7.楂樼嚎銆佷腑綰褲?佽?掑鉤鍒嗙嚎鐨勬剰涔夊拰鍋氭硶
8.涓夎?掑艦鐨勭ǔ瀹氭?э細涓夎?掑艦鐨勫艦鐘舵槸鍥哄畾鐨勶紝涓夎?掑艦鐨勮繖涓?鎬ц川鍙?涓夎?掑艦鐨勭ǔ瀹氭?с??
9.涓夎?掑艦鍐呰?掑拰瀹氱悊錛氫笁瑙掑艦涓変釜鍐呰?掔殑鍜岀瓑浜?180擄
鎺ㄨ??1鐩磋?掍笁瑙掑艦鐨勪袱涓?閿愯?掍簰浣?;
鎺ㄨ??2涓夎?掑艦鐨勪竴涓?澶栬?掔瓑浜庡拰瀹冧笉鐩擱偦鐨勪袱涓?鍐呰?掑拰;
鎺ㄨ??3涓夎?掑艦鐨勪竴涓?澶栬?掑ぇ浜庝換浣曚竴涓?鍜屽畠涓嶇浉閭?cè)潥勫唴??;
鍒濅竴涓嬪?︽湡鏁板?︾煡璇嗙偣
鐩鎬氦綰夸笌騫寵?岀嚎
涓?銆佺煡璇嗙綉緇滅粨鏋?
浜屻?佺煡璇嗚?佺偣
1銆佸湪鍚屼竴騫抽潰鍐咃紝涓ゆ潯鐩寸嚎鐨勪綅緗?鍏崇郴鏈変袱縐嶏細鐩鎬氦鍜屽鉤琛岋紝鍨傜洿鏄?鐩鎬氦鐨勪竴縐嶇壒孌婃儏鍐點??
2銆佸湪鍚屼竴騫抽潰鍐咃紝涓嶇浉浜ょ殑涓ゆ潯鐩寸嚎鍙?騫寵?岀嚎銆傚?傛灉涓ゆ潯鐩寸嚎鍙?鏈変竴涓?鍏?鍏辯偣錛岀О榪欎袱鏉＄洿綰跨浉浜?;濡傛灉涓ゆ潯鐩寸嚎娌℃湁鍏?鍏辯偣錛岀О榪欎袱鏉＄洿綰垮鉤琛屻??
3銆佷袱鏉＄洿綰跨浉浜ゆ墍鏋勬垚鐨勫洓涓?瑙掍腑錛屾湁鍏?鍏遍《鐐逛笖鏈変竴鏉″叕鍏辮竟鐨勪袱涓?瑙掓槸
閭昏ˉ瑙掋?傞偦琛ヨ?掔殑鎬ц川錛氶偦琛ヨ?掍簰琛ャ?傚?傚浘1鎵?紺猴紝涓庝簰涓洪偦琛ヨ?掞紝
涓庝簰涓洪偦琛ヨ?掋??+=180擄;+=180擄;+=180擄;
+=180擄銆?
4銆佷袱鏉＄洿綰跨浉浜ゆ墍鏋勬垚鐨勫洓涓?瑙掍腑錛屼竴涓?瑙掔殑涓よ竟鍒嗗埆鏄?鍙︿竴涓?瑙掔殑涓よ竟鐨勫弽鍚戝歡闀跨嚎錛岃繖鏍風(fēng)殑涓や釜瑙掍簰涓哄?歸《瑙掋?傚?歸《瑙掔殑鎬ц川錛氬?歸《瑙掔浉絳夈?傚?傚浘1鎵?紺猴紝涓庝簰涓哄?歸《瑙掋??=;
=銆?
5銆佷袱鏉＄洿綰跨浉浜ゆ墍鎴愮殑瑙掍腑錛屽?傛灉鏈変竴涓?鏄?鐩磋?掓垨90擄鏃訛紝縐拌繖涓ゆ潯鐩寸嚎浜掔浉鍨傜洿錛?
鍏朵腑涓?鏉″彨鍋氬彟涓?鏉＄殑鍨傜嚎銆傚?傚浘2鎵?紺猴紝褰?=90擄鏃訛紝鈯ャ??
鍨傜嚎鐨勬?ц川錛?
鎬ц川1錛氳繃涓?鐐規(guī)湁涓斿彧鏈変竴鏉＄洿綰夸笌宸茬煡鐩寸嚎鍨傜洿銆?
鎬ц川2錛氳繛鎺ョ洿綰垮?栦竴鐐逛笌鐩寸嚎涓婂悇鐐圭殑鎵?鏈夌嚎孌典腑錛屽瀭綰挎?墊渶鐭?銆?
鎬ц川3錛氬?傚浘2鎵?紺猴紝褰揳鈯?b鏃訛紝====90擄銆?
鐐瑰埌鐩寸嚎鐨勮窛紱伙細鐩寸嚎澶栦竴鐐瑰埌榪欐潯鐩寸嚎鐨勫瀭綰挎?電殑闀垮害鍙?鐐瑰埌鐩寸嚎鐨勮窛紱匯??
6銆佸悓浣嶈?掋?佸唴閿欒?掋?佸悓鏃佸唴瑙掑熀鏈?鐗瑰緛錛?
鈶犲湪涓ゆ潯鐩寸嚎(琚?鎴?綰?)鐨勫悓涓?鏂癸紝閮藉湪絎?涓夋潯鐩寸嚎(鎴?綰?)鐨勫悓涓?渚э紝榪欐牱
鐨勪袱涓?瑙掑彨鍚屼綅瑙掋?傚浘3涓?錛屽叡鏈夊?瑰悓浣嶈?掞細涓庢槸鍚屼綅瑙?;
涓庢槸鍚屼綅瑙?;涓庢槸鍚屼綅瑙?;涓庢槸鍚屼綅瑙掋??
鈶″湪涓ゆ潯鐩寸嚎(琚?鎴?綰?)涔嬮棿錛屽茍涓斿湪絎?涓夋潯鐩寸嚎(鎴?綰?)鐨勪袱渚э紝榪欐牱鐨勪袱涓?瑙掑彨鍐呴敊瑙掋?傚浘3涓?錛屽叡鏈夊?瑰唴閿欒?掞細涓庢槸鍐呴敊瑙?;涓庢槸鍐呴敊瑙掋??
鈶㈠湪涓ゆ潯鐩寸嚎(琚?鎴?綰?)鐨勪箣闂達紝閮藉湪絎?涓夋潯鐩寸嚎(鎴?綰?)鐨勫悓涓?鏃侊紝榪欐牱鐨勪袱涓?瑙掑彨鍚屾梺鍐呰?掋?傚浘3涓?錛屽叡鏈夊?瑰悓鏃佸唴瑙掞細涓庢槸鍚屾梺鍐呰??;涓庢槸鍚屾梺鍐呰?掋??
鍒濅竴鏁板?︾??涓?绔犵煡璇嗙偣鐩稿叧鏂囩珷錛?
鈽?鍒濅竴鏁板?︿笂鍐岀??涓?绔犵煡璇嗙偣褰掔撼
鈽?鍒濅竴鏁板?︿笂鍐岀??涓?绔犵煡璇嗙偣鎬葷粨
鈽?鍒濅竴鏁板?︾??涓?绔犵煡璇嗙偣鎬葷粨
鈽?鍒濅竴鏁板?︾??涓?绔犵煡璇嗙偣鎬葷粨褰掔撼
鈽?鍒濅竴鏁板?﹂噸瑕佺煡璇嗙偣鎬葷粨
鈽?鍒濅竴鏁板?︿笂鍐岀煡璇嗙偣褰掔撼
鈽?鍒濅竴鏁板?︾??1绔犳湁鐞嗘暟鐭ヨ瘑鐐規(guī)?葷粨
鈽?涓冨勾綰ф暟瀛︿笂鍐岀煡璇嗙偣鎬葷粨絎?涓?绔?
鈽?鍒濅竴鏁板?︾??涓?鍗曞厓鐭ヨ瘑鐐瑰綊綰?
鈽?鍒濅竴鏁板?︿笂鐭ヨ瘑鐐?
涓?銆佹?ｈ礋鏁?
1銆佹?ｆ暟錛氬ぇ浜?0鐨勬暟銆?
2銆佽礋鏁幫細灝忎簬0鐨勬暟銆?
3銆佹?ｆ暟澶т簬0錛岃礋鏁板皬浜?0錛屾?ｆ暟澶т簬璐熸暟銆?
娉ㄦ剰錛?0鍗充笉鏄?姝ｆ暟錛屼篃涓嶆槸璐熸暟錛?-a涓嶄竴瀹氭槸璐熸暟錛?+a涔熶笉涓?瀹氭槸姝ｆ暟錛沺涓嶆槸鏈夌悊鏁幫紱
浜屻?佹湁鐞嗘暟
1銆佹湁鐞嗘暟錛氱敱鏁存暟鍜屽垎鏁扮粍鎴愮殑鏁般?傚寘鎷?錛氭?ｆ暣鏁般??0銆佽礋鏁存暟錛屾?ｅ垎鏁般?佽礋鍒嗘暟銆傚彲浠ュ啓鎴愪袱涓?鏁翠箣姣旂殑褰㈠紡銆傦紙鏃犵悊鏁版槸涓嶈兘鍐欐垚涓や釜鏁存暟涔嬫瘮鐨勫艦寮忥紝瀹冨啓鎴愬皬鏁板艦寮忥紝灝忔暟鐐瑰悗鐨勬暟瀛楁槸鏃犻檺涓嶅驚鐜?鐨勩?傚?傦細蟺錛?
涓夈?佹暟杞?
1銆佹暟杞達細鐢ㄧ洿綰夸笂鐨勭偣琛ㄧず鏁幫紝榪欐潯鐩寸嚎鍙?鍋氭暟杞淬?傛嫤闂?錛堢敾涓?鏉＄洿綰匡紝鍦ㄧ洿綰夸笂浠誨彇涓?鐐硅〃紺烘暟0錛岃繖涓?闆剁偣鍙?鍋氬師鐐癸紝瑙勫畾鐩寸嚎涓婁粠鍘熺偣鍚戝彸鎴栧悜涓婁負姝ｆ柟鍚戠?胯觸錛涢?夊彇閫傚綋鐨勯暱搴︿負鍗曚綅闀垮害錛屼互渚塊敭琛￠ⅳ鍦ㄦ暟杞翠笂鍙栫偣銆傦級
2銆佹暟杞寸殑涓夎?佺礌錛氬師鐐廣?佹?ｆ柟鍚戙?佸崟浣嶉暱搴︺??
3銆佺浉鍙嶆暟錛氬彧鏈夌?﹀彿涓嶅悓鐨勪袱涓?鏁板彨鍋氫簰涓虹浉鍙嶆暟銆?0鐨勭浉鍙嶆暟榪樻槸0銆?
鐩稿弽鏁扮殑鍜屼負0 a+b=0 a銆乥浜掍負鐩稿弽鏁般??
鍥涖?佹湁鐞嗘暟鐨勫姞鍑忔硶
1銆佸厛瀹氱?﹀彿錛屽啀綆楃粷瀵瑰?箋??
2銆佸姞娉曡繍綆楁硶鍒欙細鍚屽彿鐩稿姞錛屽埌鐩稿悓絎﹀彿錛屽茍鎶婄粷瀵瑰?肩浉鍔犮?傚紓鍙風(fēng)浉鍔狅紝鍙栫粷瀵瑰?煎ぇ鐨勫姞鏁扮殑絎﹀彿錛屽茍鐢ㄨ緝澶х殑緇濆?瑰?煎噺鍘昏緝?yōu)畯鐨劸l濆?瑰?箋?備簰涓虹浉鍙嶆暟鐨勪袱涓?鏁扮浉鍔犲緱0銆備竴涓?鏁板悓0鐩稿姞鍑忥紝浠嶅緱榪欎釜鏁般??
浜斻?佹湁鐞嗘暟涔樻硶錛堝厛瀹氱Н鐨勭?﹀彿錛屽啀瀹氱Н鐨勫ぇ灝忥級
1銆佸悓鍙峰緱姝ｏ紝寮傚彿寰楄礋錛屽茍鎶婄粷瀵瑰?肩浉涔樸?備換浣曟暟鍚?0鐩鎬箻錛岄兘寰?0銆?
2銆佷箻縐?鏄?1鐨勪袱涓?鏁頒簰涓哄?掓暟銆?
銆?銆?鍒濅竴鏄?鎵撲笅鐭ヨ瘑鍩虹??鐨勫ソ鏃舵満錛屼負浜嗗府鍔╁悓瀛︿滑鏇村ソ鎵撲笅鐗㈠浐鐨勫?︿範鍩虹??銆備笅闈㈡槸鐢辨垜涓哄ぇ瀹舵暣鐞嗙殑鈥滃垵涓?鏁板?︾煡璇嗙偣褰掔撼鎬葷粨鈥濓紝浠呬緵鍙傝?冿紝嬈㈣繋澶у?墮槄璇匯??
銆?銆? 鍒濅竴鏁板?︾煡璇嗙偣褰掔撼鎬葷粨
銆?銆? 鍒濅竴鏁板?︾煡璇嗙偣鎬葷粨1-3绔?
銆?銆?絎?涓?绔? 鏈夌悊鏁?
銆?銆?1.1 姝ｆ暟涓庤礋鏁?
銆?銆?鍦ㄤ互鍓嶅?﹁繃鐨?0浠ュ?栫殑鏁板墠闈㈠姞涓婅礋鍙封?溾?斺?濈殑鏁板彨璐熸暟(negative number)銆?
銆?銆?涓庤礋鏁板叿鏈夌浉鍙嶆剰涔夛紝鍗充互鍓嶅?﹁繃鐨?0浠ュ?栫殑鏁板彨鍋氭?ｆ暟(positive number)(鏍規(guī)嵁闇?瑕侊紝鏈夋椂鍦ㄦ?ｆ暟鍓嶉潰涔熷姞涓娾??+鈥?)銆?
銆?銆?1.2 鏈夌悊鏁?
銆?銆?姝ｆ暣鏁般??0銆佽礋鏁存暟緇熺О鏁存暟(integer)錛屾?ｅ垎鏁板拰璐熷垎鏁扮粺縐板垎鏁?(fraction)銆?
銆?銆?鏁存暟鍜屽垎鏁扮粺縐版湁鐞嗘暟(rational number)銆?
銆?銆?閫氬父鐢ㄤ竴鏉＄洿綰夸笂鐨勭偣琛ㄧず鏁幫紝榪欐潯鐩寸嚎鍙?鏁拌醬(number axis)銆?
銆?銆?鏁拌醬涓夎?佺礌錛氬師鐐廣?佹?ｆ柟鍚戙?佸崟浣嶉暱搴︺??
銆?銆?鍦ㄧ洿綰夸笂浠誨彇涓?涓?鐐硅〃紺烘暟0錛岃繖涓?鐐瑰彨鍋氬師鐐瑰嚡鍏?(origin)銆?
銆?銆?鍙?鏈夌?﹀彿涓嶅悓鐨勪袱涓?鏁板彨鍋氫簰涓虹浉鍙嶆暟(opposite number)銆?(渚嬶細2鐨勭浉鍙嶆暟鏄?-2;0鐨勭浉鍙嶆暟鏄?0)
銆?銆?鏁拌醬涓婅〃紺烘暟a鐨勭偣涓庡師鐐圭殑璺濈?誨彨鍋氭暟a鐨勭粷瀵瑰??(absolute value),璁頒綔|a|銆?
銆?銆?涓?涓?姝ｆ暟鐨勭粷瀵瑰?兼槸瀹冩湰韜?;涓?涓?璐熸暟鐨勭粷瀵瑰?兼槸瀹冪殑鐩稿弽鏁?;0鐨勭粷瀵瑰?兼槸0銆備袱涓?璐熸暟錛岀粷瀵瑰?煎ぇ鐨勫弽鑰屽皬銆?
銆?銆?1.3 鏈夌悊鍥板瓩涓炬暟鐨勫姞鍑忔硶
銆?銆?鏈夌悊鏁板姞娉曟硶鍒欙細
銆?銆?1.鍚屽彿涓ゆ暟鐩稿姞錛屽彇鐩稿悓鐨勭?﹀彿錛屽茍鎶婄粷瀵瑰?肩浉鍔犮??
銆?銆?2.緇濆?瑰?間笉鐩哥瓑鐨勫紓鍙蜂袱鏁扮浉鍔狅紝鍙栫粷瀵瑰?艱緝澶х殑鍔犳暟鐨勭?﹀彿錛屽茍鐢ㄨ緝澶х殑緇濆?瑰?煎噺鍘昏緝?yōu)畯鐨劸l濆?瑰?箋?備簰涓虹浉鍙嶆暟鐨勪袱涓?鏁扮浉鍔犲緱0銆?
銆?銆?3.涓?涓?鏁板悓0鐩稿姞錛屼粛寰楄繖涓?鏁般??
銆?銆?鏈夌悊鏁板噺娉曟硶鍒欙細鍑忓幓涓?涓?鏁幫紝姹?紕х瓑浜庡姞榪欎釜鏁扮殑鐩稿弽鏁般??
銆?銆?1.4 鏈夌悊鏁扮殑涔橀櫎娉?
銆?銆?鏈夌悊鏁頒箻娉曟硶鍒欙細涓ゆ暟鐩鎬箻錛屽悓鍙峰緱姝ｏ紝寮傚彿寰楄礋錛屽茍鎶婄粷瀵瑰?肩浉涔樸?備換浣曟暟鍚?0鐩鎬箻錛岄兘寰?0銆?
銆?銆?涔樼Н鏄?1鐨勪袱涓?鏁頒簰涓哄?掓暟銆?
銆?銆?鏈夌悊鏁伴櫎娉曟硶鍒欙細闄や互涓?涓?涓嶇瓑浜?0鐨勬暟錛岀瓑浜庝箻榪欎釜鏁扮殑鍊掓暟銆?
銆?銆?涓ゆ暟鐩擱櫎錛屽悓鍙峰緱姝ｏ紝寮傚彿寰楄礋錛屽茍鎶婄粷瀵瑰?肩浉闄ゃ??0闄や互浠諱綍涓?涓?涓嶇瓑浜?0鐨勬暟錛岄兘寰?0銆? m矛
銆?銆?姹俷涓?鐩稿悓鍥犳暟鐨勭Н鐨勮繍綆楋紝鍙?涔樻柟錛屼箻鏂圭殑緇撴灉鍙?騫?(power)銆傚湪a鐨刵嬈℃柟涓?錛宎鍙?鍋氬簳鏁?(base number)錛宯鍙?鍋氭寚鏁?(exponent)銆?
銆?銆?璐熸暟鐨勫?囨?″箓鏄?璐熸暟錛岃礋鏁扮殑鍋舵?″箓鏄?姝ｆ暟銆傛?ｆ暟鐨勪換浣曟?″箓閮芥槸姝ｆ暟錛?0鐨勪換浣曟?″箓閮芥槸0銆?
銆?銆?鎶婁竴涓?澶т簬10鐨勬暟琛ㄧず鎴恆脳10鐨刵嬈℃柟鐨勫艦寮忥紝鐢ㄧ殑灝辨槸縐戝?﹁?℃暟娉曘??
銆?銆?浠庝竴涓?鏁扮殑宸﹁竟絎?涓?涓?闈?0鏁板瓧璧鳳紝鍒版湯浣嶆暟瀛楁??錛屾墍鏈夋暟瀛楅兘鏄?榪欎釜鏁扮殑鏈夋晥鏁板瓧(significant digit)銆?
銆?銆?絎?浜岀珷 涓?鍏冧竴嬈℃柟紼?
銆?銆?2.1 浠庣畻寮忓埌鏂圭▼
銆?銆?鏂圭▼鏄?鍚?鏈夋湭鐭ユ暟鐨勭瓑寮忋??
銆?銆?鏂圭▼閮藉彧鍚?鏈変竴涓?鏈?鐭ユ暟(鍏?)x錛屾湭鐭ユ暟x鐨勬寚鏁伴兘鏄?1(嬈?)錛岃繖鏍風(fēng)殑鏂圭▼鍙?鍋氫竴鍏冧竴嬈℃柟紼?(linear equation with one unknown)銆? 銆?銆?瑙ｆ柟紼嬪氨鏄?姹傚嚭浣挎柟紼嬩腑絳夊彿宸﹀彸涓よ竟鐩哥瓑鐨勬湭鐭ユ暟鐨勫?鹼紝榪欎釜鍊煎氨鏄?鏂圭▼鐨勮В(solution)銆?
銆?銆?絳夊紡鐨勬?ц川錛?
銆?銆?1.絳夊紡涓よ竟鍔?(鎴栧噺)鍚屼竴涓?鏁?(鎴栧紡瀛?)錛岀粨鏋滀粛鐩哥瓑銆?
銆?銆?2.絳夊紡涓よ竟涔樺悓涓?涓?鏁幫紝鎴栭櫎浠ュ悓涓?涓?涓嶄負0鐨勬暟錛岀粨鏋滀粛鐩哥瓑銆?
銆?銆?2.2 浠庡彜鑰佺殑浠ｆ暟涔﹁?磋搗鈥斺?斾竴鍏冧竴嬈℃柟紼嬬殑璁ㄨ??(1)
銆?銆?鎶婄瓑寮忎竴杈圭殑鏌愰」鍙樺彿鍚庣Щ鍒板彟涓?杈癸紝鍙?鍋氱Щ欏廣??
銆?銆?絎?涓夌珷 鍥懼艦璁よ瘑鍒濇??
銆?銆?3.1 澶氬Э澶氬僵鐨勫浘褰?
銆?銆?鍑犱綍浣撲篃綆?縐頒綋(solid)銆傚寘鍥寸潃浣撶殑鏄?闈?(surface)銆?
銆?銆?3.2 鐩寸嚎銆佸皠綰褲?佺嚎孌?
銆?銆?綰挎?靛叕鐞嗭細涓ょ偣鐨勬墍鏈夎繛綰夸腑錛岀嚎孌靛仛鐭?(涓ょ偣涔嬮棿錛岀嚎孌墊渶鐭?)銆?
銆?銆?榪炴帴涓ょ偣闂寸殑綰挎?電殑闀垮害錛屽彨鍋氳繖涓ょ偣鐨勮窛紱匯??
銆?銆?3.3 瑙掔殑搴﹂噺
銆?銆?1搴?=60鍒? 1鍒?=60縐? 1鍛ㄨ??=360搴? 1騫寵??=180搴?
銆?銆?3.4 瑙掔殑姣旇緝涓庤繍綆?
銆?銆?濡傛灉涓や釜瑙掔殑鍜岀瓑浜?90搴?(鐩磋??)錛屽氨璇磋繖涓や釜鍙?浜掍負浣欒??(compiementary angle)錛屽嵆鍏朵腑姣忎竴涓?瑙掓槸鍙︿竴涓?瑙掔殑浣欒?掋??
銆?銆?濡傛灉涓や釜瑙掔殑鍜岀瓑浜?180搴?(騫寵??)錛屽氨璇磋繖涓や釜鍙?浜掍負琛ヨ??(supplementary angle)錛屽嵆鍏朵腑姣忎竴涓?瑙掓槸鍙︿竴涓?瑙掔殑琛ヨ?掋??
銆?銆?絳夎??(鍚岃??)鐨勮ˉ瑙掔浉絳夈??
銆?銆?絳夎??(鍚岃??)鐨勪綑瑙掔浉絳夈??
銆?銆? 鍒濅竴鏁板?︾煡璇嗙偣鎬葷粨4-6绔?
銆?銆?絎?鍥涚珷 鏁版嵁鐨勬敹闆嗕笌鏁寸悊
銆?銆?鏀墮泦銆佹暣鐞嗐?佹弿榪板拰鍒嗘瀽鏁版嵁鏄?鏁版嵁澶勭悊鐨勫熀鏈?榪囩▼銆?
銆?銆?絎?浜旂珷 鐩鎬氦綰夸笌騫寵?岀嚎
銆?銆?5.1 鐩鎬氦綰?
銆?銆?瀵歸《瑙?(vertical angles)鐩哥瓑銆?
銆?銆?榪囦竴鐐規(guī)湁涓斿彧鏈変竴鏉＄洿綰夸笌宸茬煡鐩寸嚎鍨傜洿(perpendicular)銆?
銆?銆?榪炴帴鐩寸嚎澶栦竴鐐逛笌鐩寸嚎涓婂悇鐐圭殑鎵?鏈夌嚎孌典腑錛屽瀭綰挎?墊渶鐭?(綆?鍗曡?存垚錛氬瀭綰挎?墊渶鐭?)銆?
銆?銆?5.2 騫寵?岀嚎
銆?銆?緇忚繃鐩寸嚎澶栦竴鐐癸紝鏈変笖鍙?鏈変竴鏉＄洿綰夸笌榪欐潯鐩寸嚎騫寵??(parallel)銆?
銆?銆?濡傛灉涓ゆ潯鐩寸嚎閮戒笌絎?涓夋潯鐩寸嚎騫寵?岋紝閭ｄ箞榪欎袱鏉＄洿綰夸篃浜掔浉騫寵?屻??
銆?銆?鐩寸嚎騫寵?岀殑鏉′歡錛?
銆?銆?涓ゆ潯鐩寸嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽?傛灉鍚屼綅瑙掔浉絳夛紝閭ｄ箞涓ょ洿綰垮鉤琛屻??
銆?銆?涓ゆ潯鐩寸嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽?傛灉鍐呴敊瑙掔浉絳夛紝閭ｄ箞涓ょ洿綰垮鉤琛屻??
銆?銆?涓ゆ潯鐩寸嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽?傛灉鍚屾梺鍐呰?掍簰琛ワ紝閭ｄ箞涓ょ洿綰垮鉤琛屻??
銆?銆?5.3 騫寵?岀嚎鐨勬?ц川
銆?銆?涓ゆ潯騫寵?岀嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽悓浣嶈?掔浉絳夈??
銆?銆?涓ゆ潯騫寵?岀嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽唴閿欒?掔浉絳夈??
銆?銆?涓ゆ潯騫寵?岀嚎琚?絎?涓夋潯鐩寸嚎鎵?鎴?錛屽悓鏃佸唴瑙掍簰琛ャ??
銆?銆?鍒ゆ柇涓?浠朵簨鎯呯殑璇?鍙ワ紝鍙?鍋氬懡棰?(proposition)銆?
銆?銆?絎?鍏?绔? 騫抽潰鐩磋?掑潗鏍囩郴
銆?銆?6.1 騫抽潰鐩磋?掑潗鏍囩郴
銆?銆?鍚?鏈変袱涓?鏁扮殑璇嶆潵琛ㄧず涓?涓?紜?瀹氱殑浣嶇疆錛屽叾涓?涓や釜鏁板悇鑷?琛ㄧず涓嶅悓鐨勫惈涔夛紝鎴戜滑鎶婅繖縐嶆湁欏哄簭鐨勪袱涓?鏁癮鍜宐緇勬垚鐨勬暟瀵癸紝鍙?鍋氭湁搴忔暟瀵?(ordered pair)銆?
銆? 銆?鍒濅竴鏁板?︾煡璇嗙偣鎬葷粨7-10绔?
銆?銆?絎?涓冪珷 涓夎?掑艦
銆?銆?7.1 涓庝笁瑙掑艦鏈夊叧鐨勭嚎孌?
銆?銆?涓夎?掑艦(triangle)鍏鋒湁紼沖畾鎬с??
銆?銆?7.2 涓庝笁瑙掑艦鏈夊叧鐨勮??
銆?銆?涓夎?掑艦鐨勫唴瑙掑拰絳変簬180搴︺??
銆?銆?涓夎?掑艦鐨勪竴涓?澶栬?掔瓑浜庝笌瀹冧笉鐩擱偦鐨勪袱涓?鍐呰?掔殑鍜屻??
銆?銆?涓夎?掑艦鐨勪竴涓?澶栬?掑ぇ浜庝笌瀹冧笉鐩擱偦鐨勪換浣曚竴涓?鍐呰??
銆?銆?7.3 澶氳竟褰㈠強鍏跺唴瑙掑拰
銆?銆?n杈瑰艦鍐呰?掑拰絳変簬錛?(n-2)?180搴?
銆?銆?澶氳竟褰?(polygon)鐨勫?栬?掑拰絳変簬360搴︺??
銆?銆?絎?鍏?绔? 浜屽厓涓?嬈℃柟紼嬬粍
銆?銆?8.1 浜屽厓涓?嬈℃柟紼嬬粍
銆?銆?鏂圭▼涓?鍚?鏈変袱涓?鏈?鐭ユ暟(x鍜寉)錛屽茍涓旀湭鐭ユ暟鐨勬寚鏁伴兘鏄?1錛屽儚榪欐牱鐨勬柟紼嬪彨鍋氫簩鍏冧竴嬈℃柟紼?(linear equations of two unknowns) 銆?
銆?銆?鎶婁袱涓?浜屽厓涓?嬈℃柟紼嬪悎鍦ㄤ竴璧鳳紝灝辯粍鎴愪簡涓?涓?浜屽厓涓?嬈℃柟紼嬬粍(system of linear equations of two unknowns)銆?
銆?銆?浣夸簩鍏冧竴嬈℃柟紼嬩袱杈圭殑鍊肩浉絳夌殑涓や釜鏈?鐭ユ暟鐨勫?鹼紝鍙?鍋氫簩鍏冧竴嬈℃柟紼嬬殑瑙ｃ??
銆?銆?浜屽厓涓?嬈℃柟紼嬬粍鐨勪袱涓?鏂圭▼鐨勫叕鍏辮В錛屽彨鍋氫簩鍏冧竴嬈℃柟紼嬬粍鐨勮В銆?
銆?銆?8.2 娑堝厓
銆?銆?灝嗘湭鐭ユ暟鐨勪釜鏁扮敱澶氬寲灝戙?侀?愪竴瑙ｅ喅鐨勬兂娉曪紝鍙?鍋氭秷鍏冩?濇兂銆?
銆?銆?絎?涔?jié)绔?涓嶇瓑寮忎笌涓嶇瓑寮忕粍
銆?銆?9.1 涓嶇瓑寮?
銆?銆?鐢ㄥ皬浜庡彿鎴栧ぇ浜庡彿琛ㄧず澶у皬鍏崇郴鐨勫紡瀛愶紝鍙?鍋氫笉絳夊紡(inequality)銆?
銆?銆?浣夸笉絳夊紡鎴愮珛鐨勬湭鐭ユ暟鐨勫?煎彨鍋氫笉絳夊紡鐨勮В銆?
銆?銆?鑳戒嬌涓嶇瓑寮忔垚绔嬬殑x鐨勫彇鍊艱寖鍥達紝鍙?鍋氫笉絳夊紡鐨勮В鐨勯泦鍚堬紝綆?縐拌В闆?(solution set)銆?
銆?銆?鍚?鏈変竴涓?鏈?鐭ユ暟錛屾湭鐭ユ暟鐨勬?℃暟鏄?1鐨勪笉絳夊紡錛屽彨鍋氫竴鍏冧竴嬈′笉絳夊紡(linear inequality of one unknown)銆?
銆?銆?涓嶇瓑寮忕殑鎬ц川錛?
銆?銆?涓嶇瓑寮忎袱杈瑰姞(鎴栧噺)鍚屼竴涓?鏁?(鎴栧紡瀛?)錛屼笉絳夊彿鐨勬柟鍚戜笉鍙樸??
銆?銆?涓嶇瓑寮忎袱杈逛箻(鎴栭櫎浠?)鍚屼竴涓?姝ｆ暟錛屼笉絳夊彿鐨勬柟鍚戜笉鍙樸??
銆?銆?涓嶇瓑寮忎袱杈逛箻(鎴栭櫎浠?)鍚屼竴涓?璐熸暟錛屼笉絳夊彿鐨勬柟鍚戞敼鍙樸??
銆?銆?涓夎?掑艦涓?浠繪剰涓よ竟涔嬪樊灝忎簬絎?涓夎竟銆?
銆?銆?涓夎?掑艦涓?浠繪剰涓よ竟涔嬪拰澶т簬絎?涓夎竟銆?
銆?銆?9.3 涓?鍏冧竴嬈′笉絳夊紡緇?
銆?銆?鎶婁袱涓?涓?鍏冧竴嬈′笉絳夊紡鍚堝湪璧鋒潵錛屽氨緇勬垚浜嗕竴涓?涓?鍏冧竴嬈′笉絳夊紡緇?(linear inequalities of one unknown)銆?
銆?銆?絎?鍗佺珷 瀹炴暟
銆?銆?10.1 騫蟲柟鏍?
銆?銆?濡傛灉涓?涓?姝ｆ暟x鐨勫鉤鏂圭瓑浜巃錛岄偅涔堣繖涓?姝ｆ暟x鍙?鍋歛鐨勭畻鏈?騫蟲柟鏍?(arithmetic square root)錛?2鏄?鏍規(guī)寚鏁般??
銆?銆?a鐨勭畻鏈?騫蟲柟鏍硅?諱綔鈥滄牴鍙穉鈥濓紝a鍙?鍋氳??寮?鏂規(guī)暟(radicand)銆?
銆?銆?0鐨勭畻鏈?騫蟲柟鏍規(guī)槸0銆?
銆?銆?濡傛灉涓?涓?鏁扮殑騫蟲柟絳変簬a錛岄偅涔堣繖涓?鏁板彨鍋歛鐨勫鉤鏂規(guī)牴鎴栦簩嬈℃柟鏍?(square root) 銆?
銆?銆?姹備竴涓?鏁癮鐨勫鉤鏂規(guī)牴鐨勮繍綆楋紝鍙?鍋氬紑騫蟲柟(extraction of square root)銆?
銆?銆?10.2 绔嬫柟鏍?
銆?銆?濡傛灉涓?涓?鏁扮殑绔嬫柟絳変簬a,閭ｄ箞榪欎釜鏁板彨鍋歛鐨勭珛鏂規(guī)牴鎴栦笁嬈℃柟鏍?(cube root)銆?
銆?銆?姹備竴涓?鏁扮殑绔嬫柟鏍圭殑榪愮畻錛屽彨鍋氬紑绔嬫柟(extraction of cube root)銆?
銆?銆?10.3 瀹炴暟
銆?銆?鏃犻檺涓嶅驚鐜?灝忔暟鍙堝彨鍋氭棤鐞嗘暟(irrational number)銆?
銆?銆?鏈夌悊鏁板拰鏃犵悊鏁扮粺縐板疄鏁?(real number)銆?
銆?銆? 鎷撳睍闃呰?伙細鎬庢牱鎵撳ソ鍒濅竴鏁板?﹀熀紜??
銆?銆? 涓?銆佺粏蹇冨彂鎺樻?傚康鍜屽叕寮?
銆?銆?寰堝?氬悓瀛﹀?規(guī)?傚康鍜屽叕寮忎笉澶熼噸瑙嗭紝瀵規(guī)?傚康鐨勭悊瑙ｅ彧鏄?鍋滅暀鍦ㄦ枃瀛楄〃闈?銆備緥濡傦紝鍦ㄤ唬鏁板紡鐨勬?傚康涓?錛屽緢澶氬悓瀛﹀拷鐣ヤ簡鈥滃崟涓?瀛楁瘝鎴栨暟瀛椾篃鏄?浠ｆ暟寮忊??;騫朵笖瀵規(guī)?傚康鍜屽叕寮忎竴鍛崇殑姝昏?扮‖鑳岋紝緙轟箯涓庡疄闄呴?樼洰鐨勮仈緋匯?傝?佸笀鐨勫緩璁?鏄?錛氭洿緇嗗績涓?鐐?(瑙傚療鐗逛緥)錛屾洿娣卞叆涓?鐐?(浜嗚В瀹冨湪棰樼洰涓?鐨勫父瑙佽?冪偣)錛屾洿鐔熺粌涓?鐐?(鏃犺?哄畠浠ヤ粈涔堥潰鐩?鍑虹幇錛屾垜浠?閮借兘澶熷簲鐢ㄨ嚜濡?)銆?
銆?銆? 浜屻?佹?葷粨鐩鎬技綾誨瀷棰樼洰
銆?銆?褰撲綘浼氭?葷粨棰樼洰錛屽?規(guī)墍鍋氱殑棰樼洰浼氬垎綾伙紝鐭ラ亾鑷?宸辮兘澶熻В鍐沖摢浜涢?樺瀷錛屾帉鎻′簡鍝?浜涘父瑙佺殑瑙ｉ?樻柟娉曪紝榪樻湁鍝?浜涚被鍨嬮?樹笉浼氬仛鏃訛紝浣犳墠鐪熸?ｇ殑鎺屾彙浜嗚繖闂ㄥ?︾?戠殑紿嶉棬錛屾墠鑳界湡姝ｇ殑鍋氬埌鈥滀換瀹冨崈鍙樹竾鍖栵紝鎴戣嚜宀跨劧涓嶅姩鈥濄?傝繖涓?闂?棰樺?傛灉瑙ｅ喅涓嶅ソ錛屽湪榪涘叆鍒濅簩銆佸垵涓変互鍚庯紝鍚屽?︿滑浼氬彂鐜幫紝鏈変竴閮ㄥ垎鍚屽?﹀ぉ澶╁仛棰橈紝鍙?鎴愮嘩涓嶅崌鍙嶉檷銆傝?佸笀鐨勫緩璁?鏄?錛氣?滄?葷粨褰掔撼鈥濇槸灝嗛?樼洰瓚婂仛瓚婂皯鐨勬渶濂藉姙娉曘??
銆? 銆?涓夈?佹敹闆嗚嚜宸辯殑鍏稿瀷閿欒??鍜屼笉浼氱殑棰樼洰
銆?銆?鍚屽?︿滑鏈?闅鵑潰瀵圭殑錛屽氨鏄?鑷?宸辯殑閿欒??鍜屽洶闅俱?備絾榪欐伆鎭板張鏄?鏈?闇?瑕佽В鍐崇殑闂?棰樸?傚悓瀛︿滑鍋氶?樼洰錛屾湁涓や釜閲嶈?佺殑鐩?鐨勶細涓?鏄?錛屽皢鎵?瀛︾殑鐭ヨ瘑鐐瑰拰鎶?宸э紝鍦ㄥ疄闄呯殑棰樼洰涓?婕旂粌銆傚彟澶栦竴涓?灝辨槸錛屾壘鍑鴻嚜宸辯殑涓嶈凍錛岀劧鍚庡譏琛ュ畠銆傝?佸笀鐨勫緩璁?鏄?錛氬仛棰樺氨鍍忔寲閲戠熆錛屾瘡涓?閬撻敊棰橀兘鏄?涓?鍧楅噾鐭匡紝鍙?鏈夊彂鎺樸?佸喍鐐鹼紝鎵嶄細鏈夋敹鑾楓??
銆? 銆?鍥涖?佸氨涓嶆噦鐨勯棶棰橈紝縐?鏋佹彁闂?銆佽?ㄨ??
銆?銆?鍙戠幇浜嗕笉鎳傜殑闂?棰橈紝縐?鏋佸悜浠栦漢璇鋒暀銆傝繖鏄?寰堝鉤甯哥殑閬撶悊銆備絾灝辨槸榪欎竴鐐癸紝寰堝?氬悓瀛﹂兘鍋氫笉鍒般?傚師鍥犲彲鑳芥湁涓や釜鏂歸潰錛氫竴鏄?錛屽?硅?ラ棶棰樼殑閲嶈?嗕笉澶燂紝涓嶆眰鐢氳В;浜屾槸錛屼笉濂芥剰鎬濓紝鎬曢棶鑰佸笀琚?璁?錛岄棶鍚屽?﹁??鍚屽?︾灖涓嶈搗銆傝?佸笀鐨勫緩璁?鏄?錛氣?滃嫟瀛︹?濇槸鍩虹??錛屸?滃ソ闂?鈥濇槸鍏抽敭銆?
銆? 銆?浜斻?佹敞閲嶅疄鎴?(鑰冭瘯)緇忛獙鐨勫煿鍏?
銆?銆?鑰冭瘯鏈?韜?灝辨槸涓?闂ㄥ?﹂棶銆傛湁浜涘悓瀛﹀鉤鏃舵垚緇╁緢濂斤紝涓婅?捐?佸笀涓?鎻愰棶錛屼粈涔堥兘浼氥?傝?句笅鍋氶?樹篃閮戒細銆傚彲涓?鍒拌?冭瘯錛屾垚緇╁氨涓嶇悊鎯熾?傚嚭鐜拌繖縐嶆儏鍐碉紝鏈変袱涓?涓昏?佸師鍥狅細涓?鏄?錛岃?冭瘯蹇冩?佷笉涓嶅ソ錛屽?規(guī)槗绱у紶;浜屾槸錛岃?冭瘯鏃墮棿绱э紝鎬繪槸涓嶈兘鍦ㄨ?勫畾鐨勬椂闂村唴瀹屾垚銆傝?佸笀鐨勫緩璁?鏄?錛氭妸鈥滃仛浣滀笟鈥濆綋鎴愯?冭瘯錛屾妸鈥滆?冭瘯鈥濆綋鎴愬仛浣滀笟銆?
