¡¶ÊýÖá¡·ÀýÌâ½²½â
ΪÁËѧºÃÓÐÀíÊýµÄ¸ÅÄʹ˼άÊÊÓ¦Êý¼¯µÄÀ©³ä£¬ÎÒÃǰÑÏÖʵÉú»îÖдóÁ¿µÄÓйØÄ£ÐÍ£¬ÈçÖ±³ß¡¢¸Ü¸Ë¡¢Î¶ȼơ¢ÒDZíÉϵĿ̶ȣ¬Ëù¾ßÓеı¾ÖÊÊôÐÔ³éÏ󻯣¬½¨Á¢ÆðÊýÖáÄ£ÐÍ£®ÊýÖáµÄ½¨Á¢£¬¸³ÓèÁ˳éÏóµÄ´úÊý¸ÅÄîÒÔÖ±¹Û±íÏó£®
Êýѧһ¿ªÊ¼¾ÍÊÇÑо¿¡°Êý¡±ºÍ¡°ÐΡ±µÄ£¬´Ó¹ÅÏ£À°Ê±ÆÚÆð£¬ÈËÃǾÍÒÑÊÔͼ°ÑËüÃÇͳһÆðÀ´£®
ÊýÓëÐÎÓÐ×ÅÃÜÇеÄÁªÏµ£¬ÎÒÃdz£ÓôúÊýµÄ·½·¨Ñо¿Í¼ÐÎÎÊÌ⣻ÁíÒ»·½Ã棬ҲÀûÓÃͼÐÎÀ´´¦Àí´úÊýÎÊÌ⣬ÕâÖÖÊýÓëÐÎÏ໥×÷Óã¬ÊÇÒ»ÖÖÖØÒªµÄÊýѧ˼Ï롪¡ªÊýÐνáºÏ˼Ï룮 ÀûÓÃÊýÐνáºÏ˼Ïë½âÌâµÄ¹Ø¼üÊǽ¨Á¢ÊýÓëÐÎÖ®¼äµÄÁªÏµ£¬Ïֽ׶Σ¬ÊýÖáÊÇÁªÏµÊýÓëÐεÄÇÅÁº£¬Ö÷ÒªÌåÏÖÔÚ£º
1£®ÔËÓÃÊýÖáÖ±¹ÛµØ±íʾÓÐÀíÊý£» 2£®ÔËÓÃÊýÖáÐÎÏ󵨽âÊÍÏà·´Êý£»
3£®ÔËÓÃÊýÖá׼ȷµØ±È½ÏÓÐÀíÊýµÄ´óС£»
4£®ÔËÓÃÊýÖáÇ¡µ±µØ½â¾öÓë¾ø¶ÔÖµÓйØÁªµÄÎÊÌ⣮ ÀýÌâ½²½â
¡¾Àý1¡¿(1)ÊýÖáÉÏÓÐA¡¢BÁ½µã£¬Èç¹ûµãA¶ÔÓ¦µÄÊýÊÇ?2£¬ÇÒA¡¢BÁ½µãµÄ¾àÀëΪ3£¬ÄÇôµãB¶ÔÓ¦µÄÊýÊÇ £® (½ËÕÊ¡¾ºÈüÌâ)
(2)ÔÚÊýÖáÉÏ£¬µãA¡¢B·Ö±ð±íʾ?11ºÍ£¬ÔòÏß¶ÎABµÄÖеãËù±íʾµÄÊý35ÊÇ £® (½ËÕÊ¡¾ºÈüÌâ)
1ÔÚÊýÖáÉ϶ÔÓ¦µÄµã£¬Ê¹Ïß¶ÎABÑØÊýÖáÏòÓÒÒÆ¶¯µ½A?B?£¬2ÇÒÏß¶ÎA?B?µÄÖеã¶ÔÓ¦µÄÊýÊÇ3£¬ÔòµãA?¶ÔÓ¦µÄÊýÊÇ___£¬µãAÒÆ¶¯µÄ¾àÀëÊÇ
£¨3£©µãA¡¢B·Ö±ðÊÇÊý?3£¬?____£® (¡°Ï£Íû±¡±ÑûÇëÈüÊÔÌâ) ˼·µã²¦ (1)È·¶¨BµãµÄλÖã»(2)ÔÚÊýÖáÉÏÑ¡ÔñÁ½¸öÌØÊâµã£¬Ì½Ë÷ËüÃǵÄÖеãËù±íʾµÄÊýÓëËùÑ¡Á½µãËù±íʾµÄÊýµÄÁªÏµ£»£¨3£©ÔÚÆ½ÒƵĹý³ÌÖУ¬Ïß¶ÎABµÄ³¤¶È²»±ä£¬¼´AB?A?B?£® ¡¾Àý2¡¿ Èçͼ£¬ÔÚÊýÖáÉÏÓÐÁù¸öµã£¬ÇÒAB?BC?CD?DE?EF£¬ÔòÓëµãCËù±íʾµÄÊý×î½Ó½üµÄÕûÊýÊÇ________£®
˼·µã²¦ ÀûÓÃÊýÖáÌṩµÄÐÅÏ¢£¬Çó³öAFµÄ³¤¶È£® ¡¾Àý3¡¿±È½ÏaÓë
1µÄ´óС£® a11¡¢ÎÞÒâÒåµÃaa˼·µã²¦ ÒòΪa±íʾµÄÊýÓÐÈÎÒâÐÔ£¬Ö±½Ó±È½Ï³£»á·¢ÉúÒÅ©µÄÏÖÏó£¬Èô°Ñ¸÷¸ö·¶Î§ÔÚÊýÖáÉϱíʾ³öÀ´£¬½èÖúÊýÖáÌÖÂÛËüÃǵĴóС£¬ÔòÐÎÏóÖ±¹Û£¬½âÌâµÄ¹Ø¼üÊÇÓÉa??1£¬0£¬¾Ý´Ë3¸öÊý°ÑÊýÖá·ÖΪ6¸ö²¿·Ö£® ³öa?1£¬¡¾Àý4¡¿ÔĶÁÏÂÃæ²ÄÁϲ¢»Ø´ðÎÊÌ⣮ (1)ÔĶÁÏÂÃæ²ÄÁÏ£º
µãA¡¢BÔÚÊýÖáÉÏ·Ö±ð±íʾʵÊýa¡¢b£¬A¡¢BÁ½µãÖ®¼äµÄ¾àÀë±íʾΪAB£®
µ±A¡¢BÁ½µãÖÐÓÐÒ»µãÔÚÔµãʱ£¬²»·ÁÉèµã AÔÚԵ㣬Èçͼ1£¬AB?OB?b?a?b µ±A¡¢BÁ½µã¶¼²»ÔÚÔµãʱ£¬
¢ÙÈçͼ2£¬µãA¡¢B¶¼ÔÚÔµãµÄÓÒ±ßAB?OB?OA?b?a?b?a?a?b£»
¢ÚÈçͼ3£¬µãA¡¢B¶¼ÔÚÔµãµÄ×ó±ß£¬AB?OB?OA?b?a?b?a?a?b£» ¢ÛÈçͼ4£¬µãA¡¢BÔÚÔµãµÄÁ½±ß£¬AB?OB?OA?b?a??b?(?a)?a?b£» ×ÛÉÏ£¬ÊýÖáÉÏA¡¢BÁ½µãÖ®¼äµÄ¾àÀëAB?a?b£®
(2)»Ø´ðÏÂÁÐÎÊÌ⣺
¢ÙÊýÖáÉϱíʾ2ºÍ5µÄÁ½µãÖ®¼äµÄ¾àÀëÊÇ £¬ÊýÖáÉϱíʾ£2ºÍ£5µÄÁ½µãÖ®¼äµÄ¾àÀëÊÇ £¬ÊýÖáÉϱíʾ1ºÍ£3µÄÁ½µãÖ®¼äµÄ¾àÀëÊÇ £»
¢ÚÊýÖáÉϱíʾxºÍ£1µÄÁ½µãAºÍBÖ®¼äµÄ¾àÀëÊÇ ,Èç¹ûAB?2ÄÇôxΪ________£»
¢Ûµ±´úÊýʽx?1?x?2È¡×îСֵʱ£¬ÏàÓ¦µÄxµÄȡֵ·¶Î§ÊÇ £®(ÄϾ©ÊÐÖп¼Ìâ) ˼·µã²¦ ÔĶÁÀí½â´ÓÊýÖáÉÏ¿´£¬a?bµÄÒâÒ壮
Á´½Ó£º ÓÐЧµØ´ÓͼÐΡ¢Í¼±í»ñÈ¡ÐÅÏ¢ÊÇÐÅÏ¢Éç»áµÄ»ù±¾ÒªÇó£® ´ÓÊýÖáÉÏ»ñÈ¡ÓйØÐÅÏ¢ÊǽâÓÐÀíÊýÎÊÌâµÄ³£Óü¼ÇÉ£¬Ö÷Òª°üÀ¨£º ¢ÙÊýÖáÉÏÖîµãËù±íʾµÄÊýµÄÕý¸ºÐÔ£» ¢ÚÊýÖáÉϵĵ㵽ԵãµÄ¾àÀ룮
(1)×Öĸ±íʾÊýÊÇ´úÊýµÄÌØµã£¬µ«×Öĸ¾ßÓгéÏóÐÔ£¬ËùÒÔÔÚÌõ¼þÔÊÐíµÄ·¶Î§ÄÚ¸³Óè×ÖĸÒÔÌØÊâÖµÀ´¼ÆËã¡¢Åжϻò̽Çó½âÌâ˼·£¬ÄÜ»¯³éÏóΪ¾ßÌ壬Õâ¾ÍÊÇÎÒÃdz£ËµµÄ¡°¸³Öµ·¨¡±£¬µ«ÕâÖÖ·½·¨²»ÄÜ×÷Ϊ½âÌâµÄ¹æ·¶¹ý³Ì£®
(2)´¿´âµÄ´úÊý·½·¨±È½Ï³éÏó£¬ÈçÄܽèÖúͼÐÎ(ÀûÓÃÊýÐνáºÏµÄ˼Ïë·½·¨)£¬Ôò¿ÉʹÐí¶à³éÏóµÄ¸ÅÄîºÍ¸´ÔÓµÄÊýÁ¿¹ØÏµÖ±¹Û»¯¡¢ÐÎÏ󻯣¬ÉõÖÁ¼òµ¥»¯£®
¡¾Àý5¡¿ÊÔÇó£üx-1£üÊ®£üx£2£ü+£üx£3£ü+¡£üx£1997£üµÄ×îСֵ£® (Ìì½òÊоºÈüÌâ)
˼·µã²¦ ÓÉÓÚxµÄÈÎÒâÐÔ¡¢ÎÞÏÞÐÔ£¬Òò´Ë£¬Í¨¹ýÖð¸öÇó³ö´úÊýʽµÄÖµ½âÌâÃ÷ÏÔÀ§ÄÑ£¬²»·Á´Ó¾ø¶ÔÖµµÄ¼¸ºÎÒâÒ壬ÀûÓÃÊýÖáÈëÊÖ£¬½èÖú¡¾Àý4¡¿µÄ½áÂÛ½âÌ⣮
¡¾Àý6¡¿ (1)¹¤×÷Á÷Ë®ÏßÉÏ˳´ÎÅÅÁÐ5¸ö¹¤×÷̨A¡¢B¡¢C¡¢D¡¢E£¬Ò»Ö»¹¤¾ßÏäÓ¦¸Ã·ÅÔں䦣¬²ÅÄÜʹ¹¤×÷̨ÉϲÙ×÷»úÆ÷µÄÈËÈ¡¹¤¾ßËù×ߵķ³Ì×î¶Ì? (2)Èç¹û¹¤×÷̨ÓÉ5¸ö¸ÄΪ6¸ö£¬ÄÇô¹¤¾ßÏäÓ¦ÈçºÎ·ÅÖÃÄÜʹ6¸ö²Ù×÷»úÆ÷µÄÈËÈ¡¹¤¾ßËù×ߵķ³ÌÖ®ºÍ×î¶Ì?
(3)µ±Á÷Ë®ÏßÉÏÓÐn¸ö¹¤×÷̨ʱ£¬ÔõÑù·ÅÖù¤¾ßÏä×îÊÊÒË?
˼·µã²¦ °ÑÁ÷Ë®Ïß¿´×÷ÊýÖᣬ¹¤×÷̨¡¢¹¤¾ßÏä¿´×÷ÊýÖáÉϵĵ㣬ÕâÑù£¬¾ÍÕÒµ½Á˽â¾ö±¾ÀýµÄÄ£ÐÍ¡ª¡ªÊýÖᣬ½«ÎÊÌâת»¯Îª¡¾Àý4¡¿µÄÐÎʽÇó½â£®
Á´½Ó£ºÉèa1¡¢a2¡¢a3¡¢¡anÊÇÊýÖáÉÏÒÀ´ÎÅÅÁеĵã±íʾµÄÓÐÀíÊý£® ¢Ùµ±nΪżÊýʱ£¬Èôan2?x?an?12£¬Ôòx?a1?x?a2???x?anµÄÖµ×îС£»
¢Úµ±nÎªÆæÊýʱ£¬Èôx?an?1£¬Ôòx?a1?x?a2???x?anµÄÖµ×îС£®
2
»ù´¡ÑµÁ·
Ò»¡¢»ù´¡º»Êµ£º
1.ÔÚÊýÖáÉϱíʾÊýaµÄµãµ½ÔµãµÄ¾àÀëΪ,Ôòa-3=________. 2.a¡¢b¡¢cÔÚÊýÖáÉϵÄλÖÃÈçͼËùʾ£¬Ôò
111¡¢¡¢ÖÐ×î´óµÄÊÇ________. a?bc?ba?cc1abc0ba0ABCD
£¨µÚ2Ì⣩ £¨µÚ3Ì⣩ £¨µÚ4Ì⣩
3. (µÚ12½ì¡°Ï£Íû±¡±ÑûÇëÈüÊÔÌâ)ÓÐÀíÊýa¡¢b¡¢cÔÚÊýÖáÉϵÄλÖÃÈçͼËùʾ,Èôm=©¦a+b©¦-©¦b-1©¦-©¦a-c©¦-©¦1-c©¦,Ôò1000m=__________.
4.Èçͼ,¹¤×÷Á÷³ÌÏßÉÏA¡¢B¡¢C¡¢D´¦¸÷ÓÐ1Ãû¹¤ÈË,ÇÒAB=BC=CD=1,ÏÖÔÚ¹¤×÷Á÷³ÌÏßÉϰ²·ÅÒ»¸ö¹¤¾ßÏä,ʹ4¸öÈ˵½¹¤¾ßÏäµÄ¾àÀëÖ®ºÍΪ×î¶Ì,?Ôò¹¤¾ßÏäµÄ°²·ÅλÖÃÊÇ__________. 5.ÓÐÀíÊýa¡¢b¡¢cÔÚÊýÖáÉϵÄλÖÃÈçͼ£¬»¯¼ò©¦a+b©¦-©¦c-b©¦µÄ½á¹ûΪ( )
A.a+c B.-a-2b+c C.a+2b-c D.-a-c
ca0bA
BCDADOCB
£¨µÚ5Ì⣩ £¨µÚ6Ì⣩ £¨µÚ8Ì⣩
6. (µÚ15½ì½ËÕÊ¡¾ºÈüÌâ)Èçͼ,ÊýÖáÉϱê³öÈô¸É¸öµã,ÿÏàÁÚÁ½µãÏà¾à1¸öµ¥Î»,µãA¡¢B¡¢C¡¢D¶ÔÓ¦µÄÊý·Ö±ðÊÇÕûÊýa,b,c,d,ÇÒd-2a=10,ÄÇôÊýÖáµÄÔµãÓ¦ÊÇ( ). A.Aµã B.Bµã C.Cµã D.Dµã 7.©¦x+1©¦+©¦x-1©¦µÄ×îСֵÊÇ( ). A.2 B.0 C.1 D.-1 8. (µÚ18½ì½ËÕÊ¡¾ºÈüÌâ)Êýa¡¢b¡¢c¡¢dËù¶ÔÓ¦µÄµãA¡¢B¡¢C¡¢DÔÚÊýÖáÉϵÄλÖÃÈçͼËùʾ,ÄÇôa+cÓëb+dµÄ´óС¹ØÏµÊÇ( ).
A.a+cb+d D.²»È·¶¨µÄ
9. (±±¾©ÊС°Ó´º±¡±¾ºÈüÌâ)ÒÑÖªÊýÖáÉÏÓÐA¡¢BÁ½µã£¬A¡¢BÖ®¼äµÄ¾àÀëΪ1,µãAÓëÔµãOµÄ¾àÀëΪ3,ÇóËùÓÐÂú×ãÌõ¼þµÄµãBÓëÔµãOµÄ¾àÀëµÄºÍ.
10.ÒÑÖªÁ½Êýa¡¢b,Èç¹ûa±Èb´ó,ÊÔÅжϩ¦a©¦Ó멦b©¦µÄ´óС.
¶þ¡¢ÄÜÁ¦ÍØÕ¹
11.ÓÐÀíÊýa¡¢bÂú×ãa>0,b<0,©¦a©¦<©¦b©¦,Óá°¡´¡±½«a¡¢b¡¢-a¡¢-b?Á¬½ÓÆðÀ´_________. 12.©¦x+1©¦+©¦x-2©¦+©¦x-3©¦µÄ×îСֵÊÇ_________.
13.ÒÑÖªÊýÖáÉϱíʾ¸ºÓÐÀíÊýmµÄµãÊǵãM,ÄÇôÔÚÊýÖáÉÏÓëµãMÏà¾à©¦m©¦¸öµ¥Î»µÄµãÖÐ,ÓëÔµã¾àÀë½ÏÔ¶µÄµã¶ÔÓ¦µÄÊýÊÇ________. (2001Äêɽ¶«Ê¡¾ºÈüÌâ)