¡¾±Ø×öÌâ¡¿µÚ22Ìâ¡¢µÚ23Ìâ.ÿÌâ10·Ö.¹²¼Æ20·Ö.ÇëÔÚ´ðÌ⿨ָ¶¨Çø±ÏÄÚ×÷´ð.½â´ðʱӦд³öÎÄ×Ö˵Ã÷¡¢Ö¤Ã÷¹ý³Ì»òÑÝËã²½Öè. 22.(±¾Ð¡ÌâÂú·Ö10·Ö)
ijУ¿ªÉè8ÃÅУ±¾¿Î³Ì£¬ÆäÖÐ4ÃſγÌΪÈËÎÄ¿ÆÑ§£¬4ÃÅΪ×ÔÈ»¿ÆÑ§£¬Ñ§Ð£ÒªÇóѧÉúÔÚ¸ßÖÐÈýÄêÄÚ´ÓÖÐÑ¡ÐÞ3Ãſγ̣¬¼ÙÉèѧÉúÑ¡ÐÞÿÃſγ̵Ļú»á¾ùµÈ. (1)ÇóijͬѧÖÁÉÙÑ¡ÐÞ1ÃÅ×ÔÈ»¿ÆÑ§¿Î³ÌµÄ¸ÅÂÊ;
(2)ÒÑ֪ijͬѧËùÑ¡ÐÞµÄ3ÃſγÌÖÐÓÐ1ÃÅÈËÎÄ¿ÆÑ§£¬2ÃÅ×ÔÈ»¿ÆÑ§£¬Èô¸Ãͬѧͨ¹ýÈËÎÄ¿ÆÑ§¿Î³ÌµÄ¸ÅÂʶ¼ÊÇ
43£¬×ÔÈ»¿ÆÑ§¿Î³ÌµÄ¸ÅÂʶ¼ÊÇ£¬ÇÒ¸÷ÃſγÌͨ¹ýÓë·ñÏ໥¶ÀÁ¢.ÓÃ?±íʾ¸ÃͬѧËùÑ¡µÄ3ÃſγÌ54ͨ¹ýµÄÃÅÊý£¬ÇóËæ»ú±äÁ¿?µÄ¸ÅÂÊ·Ö²¼ÁкÍÊýѧÆÚÍû¡£
23.(±¾Ð¡ÌâÂú·Ö10·Ö)
ÔÚÆ½ÃæÖ±½Ç×ø±êϵxOyÖУ¬ÒÑÖªÅ×Îï y?2px(p?0)µÄ×¼Ïß·½³ÌΪ x??21,¹ýµãM(0,-2)×÷Å×Îï4ÏßµÄÇÐÏßMA£¬ÇеãΪA£¨ÒìÓÚµãO).Ö±Ïßl¹ýµãMÓëÅ×ÎïÏß½»ÓÚÁ½µãB,C£¬ÓëÖ±ÏßOA½»ÓÚµãN. (1)ÇóÅ×ÎïÏߵķ½³Ì; (2)ÊÔÎÊ:
MNMNµÄÖµÊÇ·ñΪ¶¨Öµ£¿ÈôÊÇ£¬Çó³ö¶¨Öµ£»Èô²»ÊÇ£¬ËµÃ÷ÀíÓÉ¡£ ?MBMC
5 / 14
²Î¿¼´ð°¸ÓëÆÀ·Ö±ê×¼
Ò»¡¢Ìî¿ÕÌ⣺£¨±¾´óÌâ¹²14СÌ⣬ÿСÌâ5·Ö£¬¹²¼Æ70·Ö£®²»Ðèд³ö½âÌâ¹ý³Ì£¬Çë°Ñ´ð°¸Ö±½ÓÌîдÔÚ´ð£®Ì⿨ÏàӦλÖÃÉÏ£© £®£®£®£®£®£®£®
3145£» 4£®£» 5£®7£» 6£®¦Ð£» 7£®?2£»
33618£®22£» 9£®18£» 10£®£» 11£®2£» 12£®25 £» 13£®(??,3]£» 14£®3£®
2¶þ¡¢½â´ðÌâ: ±¾´óÌâ¹²6СÌ⣬ 15~17ÿСÌâ14·Ö£¬18~20ÿСÌâ16·Ö£¬¹²¼Æ90·Ö£®ÇëÔÚ´ðÌ⿨ָ¶¨£®£®£®£®£®
1£®6£» 2£®?3£» 3£®
µÄÇøÓòÄÚ×÷´ð£¬½â´ðʱӦд³öÎÄ×Ö˵Ã÷¡¢Ö¤Ã÷¹ý³Ì»òÑÝËã²½Ö裮 £®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®£®15£®(1)ÒòΪa?b£¬ËùÒÔagb=0£¬ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡2·Ö
ËùÒÔ2sin??sin?????53¦Ð?sin??cos??0£® ¡¡¡¡¡¡¡4·Ö ?0£¬¼´?223?ÒòΪcos??0£¬ËùÒÔtan???(2)ÓÉa¡Îb£¬µÃ2sin?sin???¼´2sin?cos23£® ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡6·Ö 5??¦Ð???1£¬ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡8·Ö 3?13¦Ð¦Ðsin2??1£¬ ?2sin?cos?sin?1£¬¼´?1?cos2???2233ÕûÀíµÃ£¬sin?2??ÓÖ???0,ËùÒÔ2????¦Ð?1?? ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡11·Ö 6?2??¦Ð?¦Ð?¦Ð5¦Ð?2?????,?£¬ £¬ËùÒÔ?2?6?66?¦Ð¦Ð¦Ð
?£¬¼´??£® ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡14·Ö 666
16£®£¨1£©ÒòÎªÆ½ÃæPBC¡ÍÆ½ÃæABC£¬Æ½ÃæPBCIÆ½ÃæABC?BC£¬AB?Æ½ÃæABC£¬
AB¡ÍBC£¬ËùÒÔAB¡ÍÆ½ÃæPBC£® ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡2·Ö
ÒòΪCP?Æ½ÃæPBC£¬ËùÒÔCP¡ÍAB. ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡4·Ö ÓÖÒòΪCP¡ÍPB£¬ÇÒPBIAB?B£¬AB,PB?Æ½ÃæPAB,
ËùÒÔCP¡ÍÆ½ÃæPAB£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡6·Ö ÓÖÒòΪPA?Æ½ÃæPAB£¬ËùÒÔCP¡ÍPA£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡7·Ö £¨2£©ÔÚÆ½ÃæPBCÄÚ¹ýµãP×÷PD¡ÍBC£¬´¹×ãΪD£®¡¡¡¡¡¡¡¡¡¡¡¡¡8·Ö
ÒòÎªÆ½ÃæPBC¡ÍÆ½ÃæABC£¬ÓÖÆ½ÃæPBC¡ÉÆ½ÃæABC£½BC£¬
PD?Æ½ÃæPBC£¬ËùÒÔPD¡ÍÆ½ÃæABC£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡10·Ö
ÓÖl¡ÍÆ½ÃæABC£¬ËùÒÔl//PD£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡12·Ö ÓÖl?Æ½ÃæPBC£¬PD?Æ½ÃæPBC£¬l//Æ½ÃæPBC£®¡¡¡¡14·Ö
6 / 14
A
P C D
B
17£®(1) ÒòΪA(?3,4)£¬ËùÒÔOA?(?3)2?42?5£¬¡¡¡¡¡¡¡¡¡¡¡¡¡1·Ö
ÓÖÒòΪAC?4£¬ËùÒÔOC?1£¬ËùÒÔC(?,)£¬¡¡¡¡¡¡¡¡¡¡¡¡¡3·Ö ÓÉBD?4£¬µÃD(5,0)£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ 4·Ö
345545??1ËùÒÔÖ±ÏßCDµÄбÂÊ£¬ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡5·Ö
7?3?5?????5?0?ËùÒÔÖ±ÏßCDµÄ·½³ÌΪy??(x?5)£¬¼´x?7y?5?0£®¡¡¡¡¡¡¡¡¡¡6·Ö £¨2)ÉèC(?3m,4m)(0?m¡Ü1)£¬ÔòOC?5m£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡7·Ö
ÔòAC?OA?OC?5?5m£¬
ÒòΪAC?BD£¬ËùÒÔOD?OB?BD?5m+4£¬
ËùÒÔDµãµÄ×ø±êΪ (5m+4,0) ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡8·Ö ÓÖÉè?OCDµÄÍâ½ÓÔ²µÄ·½³ÌΪx?y?Dx+Ey?F?0£¬
2217?F?0,??22ÔòÓÐ?9m?16m?3mD?4mE?F?0,¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡10·Ö
?25m?4??5m?4?D?F?0.????½âÖ®µÃD??(5m?4),F?0,E??10m?3,
ËùÒÔ?OCDµÄÍâ½ÓÔ²µÄ·½³ÌΪx?y?(5m?4)x?(10m?3)y?0£¬¡¡¡¡12·Ö ÕûÀíµÃx2?y2?4x?3y?5m(x?2y)?0£¬
22?x2?y2?4x?3y=0,?x?0,?x?2, Áî?£¬ËùÒÔ?£¨Éᣩ»ò??y?0.?y??1.?x+2y=0ËùÒÔ¡÷OCDµÄÍâ½ÓÔ²ºã¹ý¶¨µãΪ(2,?1)£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡14·Ö
18£®(1)Èçͼ£¬ÒÔAÎª×ø±êÔµãO£¬ABËùÔÚÖ±ÏßΪxÖᣬ½¨Á¢Æ½ÃæÖ±½Ç×ø±êϵ£¬ÔòCµã×ø±êΪ
(2,4)£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡1·Ö
Éè±ßÔµÏßACËùÔÚÅ×ÎïÏߵķ½³ÌΪy=ax2£¬ °Ñ(2,4)´úÈ룬µÃ4=a?22£¬½âµÃa=1£¬
ËùÒÔÅ×ÎïÏߵķ½³ÌΪy=x2£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡3·Ö ÒòΪy¡é=2x£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡4·Ö
7 / 14
ËùÒÔ¹ýP(t,t2)µÄÇÐÏßEF·½³ÌΪy=2tx-t2£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡5·Ö Áîy=0£¬µÃE(,0)£»Áîx=2£¬µÃF(2,4t-t2)£¬¡¡¡¡¡¡¡¡¡¡¡¡¡7·Ö
t21t(2?)(4t?t2)£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡8·Ö 22132ËùÒÔS?(t?8t?16t)£¬¶¨ÒåÓòΪ(0,2]£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡9·Ö
41234(2)S??(3t?16t?16)?(t?4)(t?)£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡12·Ö
4434ÓÉS?(t)?0£¬µÃ0?t?£¬
y 3C D 44ËùÒÔS?(t)ÔÚ(0,)ÉÏÊÇÔöº¯Êý£¬ÔÚ(,2]ÉÏÊǼõº¯Êý£¬¡¡14·Ö F 33464ËùÒÔSÔÚ(0,2]ÉÏÓÐ×î´óÖµS()?£®
3276417P ÓÖÒòΪ?3??3£¬ 2727ËùÒÔ²»´æÔÚµãP£¬Ê¹¸ôÀë³öµÄ¡÷BEFÃæ»ýS³¬¹ý3km2£®¡16·Ö ËùÒÔS?19£®£¨1£©ÒòΪan?an?2???2an?1£¬a1?a2?1£¬
ËùÒÔa3?2a2-a1+????1£¬
ͬÀí£¬a4?2a3-a2+??3??1£¬a5?2a4-a3+??6??1£¬ ¡¡¡¡¡¡¡¡2·Ö ÓÖÒòΪa4?a1?3?£¬a5?a4?3?£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡3·Ö ËùÒÔa4?a1?a5?a4£¬
¹Êa1£¬a4£¬a5³ÉµÈ²îÊýÁУ®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡4·Ö £¨2£© ÓÉan?an?2???2an?1£¬µÃan?2?an?1?an?1?an+?£¬¡¡¡¡¡¡¡¡¡¡5·Ö
Áîbn?an?1?an£¬Ôòbn?1?bn??£¬b1?a2?a1?0£¬ ËùÒÔ?bn?ÊÇÒÔ0ΪÊ×Ï¹«²îΪ?µÄµÈ²îÊýÁУ¬
ËùÒÔbn?b1?(n?1)??(n?1)?£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡6·Ö ¼´an?1?an?(n?1)?£¬
ËùÒÔan?2?an?2(an?1?an)???(2n?1)?£¬ ËùÒÔcn?2an?2?anO(A) E £¨µÚ18Ì⣩
B x ?2(2n?1)?£® ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡8·Ö
8 / 14