·¢²¼Ê±¼ä : ÐÇÆÚÈÕ ÎÄÕ¸£½¨Ê¡¸£ÖÝÊÐ2018½ì¸ßÈý3ÔÂÖÊÁ¿¼ì²âÊýѧÀíÊÔÌâ¸üÐÂÍê±Ï¿ªÊ¼ÔĶÁ75eb21227b563c1ec5da50e2524de518964bd328
2018 Ä긣ÖÝÊиßÖбÏÒµ°àÖÊÁ¿¼ì²â
Êý ѧ £¨ Àí ¿Æ £© ÊÔ ¾í
±¾ÊÔ¾í¹² 4 Ò³£¬23 Ì⡣ȫ¾íÂú·Ö 150 ·Ö£¬¿¼ÊÔÓÃʱ 120 ·ÖÖÓ¡£ ×¢ÒâÊÂÏ
1£®´ðÌâÇ°£¬¿¼ÉúÎñ±ØÔÚÊÔÌâ¾í¡¢´ðÌ⿨¹æ¶¨µÄµØ·½Ìîд×Ô¼ºµÄ×¼¿¼Ö¤ºÅ¡¢ÐÕÃû£®¿¼ ÉúÒªÈÏÕæºË¶Ô´ðÌ⿨ÉÏÕ³ÌùµÄÌõÐÎÂëµÄ¡°×¼¿¼Ö¤ºÅ¡¢ÐÕÃû¡±Ó뿼Éú±¾ÈË×¼¿¼Ö¤ºÅ¡¢ÐÕÃûÊÇ ·ñÒ»Ö¡£
2£®µÚ¢ñ¾íÿСÌâÑ¡³ö´ð°¸ºó£¬Óà 2B Ǧ±Ê°Ñ´ðÌ⿨É϶ÔÓ¦ÌâÄ¿µÄ´ð°¸±êºÅÍ¿ºÚ¡£ÈçÐè ¸Ä¶¯£¬ÓÃÏðƤ²Á¸É¾»ºó£¬ÔÙÑ¡Í¿ÆäËü´ð°¸±êºÅ¡£µÚ¢ò¾íÓà 0.5 ºÁÃ׺ÚÉ«Ç©×Ö±ÊÔÚ´ðÌ⿨ÉÏ Êéд×÷´ð¡£ÔÚÊÔÌâ¾íÉÏ×÷´ð£¬´ð°¸ÎÞЧ¡£
3£®¿¼ÊÔ½áÊø£¬¿¼Éú±ØÐ뽫ÊÔÌâ¾íºÍ´ðÌ⿨һ²¢½»»Ø¡£
µÚ ¢ñ ¾í
Ò»¡¢Ñ¡ÔñÌ⣺±¾´óÌâ¹² 12 СÌ⣬ÿСÌâ 5 ·Ö£¬ÔÚÿСÌâ¸ø³öµÄËĸöÑ¡ÏîÖУ¬Ö»ÓÐÒ»ÏîÊÇ
·ûºÏÌâÄ¿ÒªÇóµÄ¡£ (1) ÒÑÖª¸´Êý z Âú×ã z ¶ÔÓ¦µÄµãλÓÚ ?i ? 1? z ? ?2 £¬ÔòÔÚ¸´Æ½ÃæÄÚ£¬
£¨A£©µÚÒ»ÏóÏÞ £¨B£©µÚ¶þÏóÏÞ £¨C£©µÚÈýÏóÏÞ £¨D£©µÚËÄÏóÏÞ
(2) ΪÁ˽âijµØÇøµÄ¡°Î¢ÐŽ¡²½×ß¡±»î¶¯Çé¿ö£¬Äâ´Ó¸ÃµØÇøµÄÈËȺÖгéÈ¡²¿·ÖÈËÔ±½øÐе÷
²é£¬ÊÂÏÈÒÑÁ˽⵽¸ÃµØÇøÀÏ¡¢ÖС¢ÇàÈý¸öÄêÁä¶ÎÈËÔ±µÄ¡°Î¢ÐŽ¡²½×ß¡±»î¶¯Çé¿öÓÐ½Ï ´ó²îÒ죬¶øÄÐÅ®¡°Î¢ÐŽ¡²½×ß¡±»î¶¯Çé¿ö²îÒì²»´ó£®ÔÚÏÂÃæµÄ³éÑù·½·¨ÖУ¬×îºÏÀíµÄ ³éÑù·½·¨ÊÇ
£¨A£©¼òµ¥Ëæ»ú³éÑù £¨B£©°´ÐÔ±ð·Ö²ã³éÑù £¨C£©°´ÄêÁä¶Î·Ö²ã³éÑù £¨D£©ÏµÍ³³éÑù (3) ÒÑ֪˫ÇúÏß E £º mx 2 ? y 2 ? 1 µÄÁ½¶¥µã¼äµÄ¾àÀëΪ 4£¬Ôò E µÄ½¥½üÏß·½³ÌΪ
xx£¨A£©y??£¨B£©y??£¨C£©y??2x£¨D£©y??x42
(4) Èô½Ç? µÄ¶¥µãÓëÔµãÖغϣ¬Ê¼±ßÓë x ÖáµÄ·Ç¸º°ëÖáÖغϣ¬ÖÕ±ßÔÚÖ±Ïßy?3x4
ÉÏ£¬Ôòcos 2? ? £¨A£©
72417£¨C£©£¨D£©-£¨B£©2572525 (5) ÒÑÖªÈýÀâ׶ P ? ABC µÄËĸö¶¥µã¶¼ÔÚÇò O µÄ±íÃæÉÏ£¬ PA ? ƽÃæ ABC £¬ AB ? BC £¬ÇÒ PA ? 8 £®ÈôƽÃæ ABC ½ØÇò O ËùµÃ½ØÃæµÄÃæ»ýΪ 9? £¬ÔòÇò O µÄ±íÃæ»ýΪ £¨A£©10?? £¨B£© £¨C£© £¨D£©100??25?? 50?? (6) º¯Êý f ? x ? ? x2 ? ln ?e ? x ? ln ?e ? x ? µÄͼÏó´óÖÂΪ
y
y
y y
-e
1
1
e
x -e
O
1
O
e x
-e
O
e x -e O e x
£¨A£©
£¨B£© £¨C£© £¨D£©
ÊýѧÊÔÌ⣨µÚ 1 Ò³¹² 4 Ò³£©
1 (7) ÓÒÃæ³ÌÐò¿òͼÊÇΪÁËÇó³öÂú×ã1 ? 1 ? 1 ??n ? ? 1 000 µÄ×î´óÕýÕûÊý
2 3 n
¿ªÊ¼ i ? 1, S ? 0 µÄÖµ£¬ÄÇôÔÚ
ºÍ Á½¸ö¿Õ°×¿òÖУ¬¿ÉÒÔ·Ö±ðÌîÈë
£¨A£©¡° S ? 1 000 ¡±ºÍ¡°Êä³ö i ? 1 ¡± £¨B£©¡° S ? 1 000 ¡±ºÍ¡°Êä³ö i ? 2 ¡±
1S ? S ? i i ? i ? 1 ·ñÊÇ
£¨C£©¡° S 1 000 ¡±ºÍ¡°Êä³ö i ? 1 ¡± £¨D£©¡° S 1 000 ¡±ºÍ¡°Êä³ö i ? 2 ¡±
(8) ¸£ÖÝÎ÷ºþ¹«Ô°»¨Õ¹Æڼ䣬°²ÅÅ 6 λ־ԸÕßµ½ 4 ¸öÕ¹ÇøÌṩ·þÎñ£¬ÒªÇó
£¨A£©90 ÖÖ £¨B£©180 ÖÖ
£¨C£©270 ÖÖ £¨D£©360 ÖÖ
½áÊø ¼×¡¢ÒÒÁ½¸öÕ¹Çø¸÷°²ÅÅÒ»¸öÈË£¬Ê£ÏÂÁ½¸öÕ¹Çø¸÷°²ÅÅÁ½¸öÈË£¬²»Í¬µÄ°²ÅÅ·½°¸¹²ÓÐ (9) Èçͼ£¬Íø¸ñÖ½ÉÏСÕý·½Ðεı߳¤Îª1 £¬´ÖʵÏß»³öµÄÊÇij¼¸ºÎÌå
µÄÈýÊÓͼ£¬Ôò¸Ã¼¸ºÎÌåµÄÌå»ýΪ
??2?+6£¨C£©+6£¨D£©+2 333x?0?0f ? x2 ? 2? ? f ? x ? µÄ ÔòÂú×ã x µÄ(10) É躯Êý f ( x) ??x,?x2?2xf0?£¨A£©?+6£¨B£©
È¡Öµ·¶Î§ÊÇ
£¨A£© (??, ?1) (2, ??)
£¨B£© (??, ??2 ) ( 2 , ??) £¨D£© (??, ?1) ( 2 , ??)
£¨C£© (??, ??2 ) (2, ??)
C£ºy 2 ? 2 px( p ? 0) µÄ½¹µãΪ F £¬×¼ÏßΪ F µÄ (11) ÔÚƽÃæÖ±½Ç×ø±êϵ xOy ÖУ¬Å×ÎïÏß l £®¹ý
Ö±Ïß½» A, B Á½µã£¬½» l ÓÚµã E £¬Ö±Ïß l ÓÚµã D .Èô BE ? 2 BF £¬ÇÒ AF ? 3 £¬ C ÓÚ AO ½»
Ôò BD =
£¨A£©1 £¨B£©3 £¨C£©3 »ò 9 £¨D£©1 »ò 9
(12) ÒÑÖªº¯Êý f ? x ? ? sin 2 x µÄͼÏóÓëÖ±Ïß 2kx ? 2 y ? k ¦Ð ? 0 ? k ? 0? Ç¡ÓÐÈý¸ö¹«¹²µã£¬ÕâÈý
x1 , x2 , x3 £¬Ôò ¸öµãµÄºá×ø±ê´ÓСµ½´ó·Ö±ðΪ ? x1 ? x3 ? tan ? x2 ? 2 x3 ? ??
£¨A£© ? 2
£¨B£© ?1 £¨C£©0 £¨D£©1
ÊýѧÊÔÌ⣨µÚ 2 Ò³¹² 4 Ò³£©
µÚ¢ò¾í
±¾¾í°üÀ¨±Ø¿¼ÌâºÍÑ¡¿¼ÌâÁ½²¿·Ö¡£µÚ (13)¡«(21) ÌâΪ±Ø¿¼Ì⣬ÿ¸öÊÔÌ⿼Éú¶¼±Ø
Ðë ×÷´ð¡£µÚ (22) ¡¢(23) ÌâΪѡ¿¼Ì⣬¿¼Éú¸ù¾ÝÒªÇó×÷´ð¡£ ¶þ¡¢Ìî¿ÕÌ⣺±¾´óÌâ¹² 4 СÌ⣬ÿСÌâ 5 ·Ö£® (13) ÒÑÖª¼¯ºÏ A ? ?1, 3, 4, 7?, B ? ?x x ? 2k ? 1, k ? A? £¬Ôò¼¯ºÏ A B ÖÐÔªËصĸöÊýΪ
AB ? 3, BC ??3, A ? 30? £¬Ôò¡÷ABC µÄÃæ»ýΪ (14) ÔÚ¶Û½ÇÈý½ÇÐÎ ABC ÖУ¬ x, ?? y
?
(15) Éè±äÁ¿ x, y Âú×ãÔ¼ÊøÌõ¼þ x ? 2 y 3, Ôò z ? 2 x ? 2 y µÄÈ¡Öµ A ??
? 2 x ? y 6, ??
. .
·¶Î§Îª .
B
D C (16) Èç ͼ £¬ ÔÚ Æ½ Ãæ ËÄ ±ß ÐÎ ABCD ÖУ¬ ?ABC ? 90? £¬
x, y ? R ? £¬Ôò x ? y µÄ ?DCA ? 2?BAC £®Èô BD ? xBA ? y BC ?
ֵΪ
.
Èý¡¢½â´ðÌ⣺½â´ðӦд³öÎÄ×Ö˵Ã÷¡¢Ö¤Ã÷¹ý³Ì»òÑÝËã²½Öè¡£
(17) £¨±¾Ð¡ÌâÂú·Ö 12 ·Ö£© ÒÑÖªµÈ²îÊýÁÐ?an ? µÄÇ° n ÏîºÍΪ Sn £¬ a1 ? 2 £¬ÇÒ£¨1£©Çó an £»
£¨2£©Èôbn?an?4SnanS10S5=+5105
nÏîµÄºÍTn ÇóÊýÁÐ{b n} µÄÇ°
C £¬
(18) £¨±¾Ð¡ÌâÂú·Ö 12 ·Ö£©
ÔÚÖ±ÈýÀâÖù ABC ? A1 B1C1 ÖУ¬¡÷ABC ΪÕýÈý½ÇÐΣ¬µã D ÔÚÀâ BC ÉÏ£¬ÇÒ E , F ·Ö±ðΪÀâ AB , BB1 µÄÖеã. CD ? 3BD £¬µã
A1C¡ÎƽÃæ £¨1£©Ö¤Ã÷£º DEF £»
A1C ? EF £¬ÇóÖ±Ïß A1C1 ÓëƽÃæ £¨2£©Èô DEF Ëù³ÉµÄ½ÇµÄÕýÏÒÖµ£® (19) £¨±¾Ð¡ÌâÂú·Ö 12 ·Ö£©
´Óij¼¼Êõ¹«Ë¾¿ª·¢µÄijÖÖ²úÆ·ÖÐËæ»ú³éÈ¡ 200 ¼þ£¬²âÁ¿ÕâЩ²úÆ·µÄÒ»ÏîÖÊÁ¿Ö¸±êÖµ£¨¼Ç Ϊ Z £©£¬ÓɲâÁ¿½á¹ûµÃÈçÏÂƵÂÊ·Ö²¼Ö±·½Í¼£º
Z £© £¨
ÊýѧÊÔÌ⣨µÚ 3 Ò³¹² 4 Ò³£©
£¨1£©¹«Ë¾¹æ¶¨£ºµ± Z 95 ʱ£¬²úƷΪÕýÆ·£»µ± Z ? 95 ʱ£¬²úƷΪ´ÎÆ·£®¹«Ë¾Ã¿Éú²ú Ò»¼þÕâÖÖ²úÆ·£¬ÈôÊÇÕýÆ·£¬ÔòÓ¯Àû 90 Ôª£»ÈôÊÇ´ÎÆ·£¬Ôò¿÷Ëð 30 Ôª£®¼Ç? ΪÉú²úÒ»¼þÕâÖÖ ²úÆ·µÄÀûÈó£¬ÇóËæ»ú±äÁ¿? µÄ·Ö²¼ÁкÍÊýѧÆÚÍû£»
2
£¨2£©ÓÉƵÂÊ·Ö²¼Ö±·½Í¼¿ÉÒÔÈÏΪ£¬ Z ·þ´ÓÕý̬·Ö²¼ N ? ? ,? ? £¬ÆäÖÐ ? ½üËÆΪÑù±¾Æ½
¾ùÊý x £¬? 2 ½üËÆΪÑù±¾·½²î s 2 £¨Í¬Ò»×éÖеÄÊý¾ÝÓøÃÇø¼äµÄÖеãÖµ×÷´ú±í£©£®
P ?87.8 ? Z ? 112.2 ? £» ¢ÙÀûÓøÃÕý̬·Ö²¼£¬Çó
¢Úij¿Í»§´Ó¸Ã¹«Ë¾¹ºÂòÁË 500 ¼þÕâÖÖ²úÆ·£¬¼Ç X ±íʾÕâ 500 ¼þ²úÆ·ÖиÃÏîÖÊÁ¿Ö¸±êÖµ E ? X ? £® λÓÚÇø¼ä ?87.8,112.2 ? µÄ²úÆ·¼þÊý£¬ÀûÓâٵĽá¹û£¬Çó
¸½£º 150 ? 12.2.
N (? ,? 2 ) £¬Ôò Èô Z ¡« P(? ? ? ? Z ? ? ? ? ) =0.6826£¬ P(? ? 2? ? Z ? ? ? 2? ) =0.9544.
(20) £¨±¾Ð¡ÌâÂú·Ö 12 ·Ö£©
2 2
A ΪԲ A ÔÚ M Âú×ã Éèµã C : x? y ? 4 ÉϵĶ¯µã£¬µã x ÖáÉϵÄͶӰΪ Q £®¶¯µã
M µÄ¹ì¼£Îª E . 2MQ ? AQ £¬¶¯µã
£¨1£©Çó E µÄ·½³Ì£»
£¨2£©Éè E Óë y ÖáÕý°ëÖáµÄ½»µãΪ B£¬¹ýµã B µÄÖ±Ïß E ½» l µÄбÂÊΪ k (k ? 0) £¬ l Óë
ÓÚÁíÒ»µãΪ P.ÈôÒÔµã B ΪԲÐÄ£¬ÒÔÏ߶ΠBP ³¤Îª°ë¾¶µÄÔ²Óë E ÓÐ 4 ¸ö¹«¹²µã£¬Çó k µÄ È¡Öµ·¶Î§.
(21) £¨±¾Ð¡ÌâÂú·Ö 12 ·Ö£©
£¨1£©Çóº¯Êý f (x) ? x ln x ? a(a ? 0) µÄÁãµã¸öÊý£» g ( x) ? 2 x 2 ln x ? x 2 ? ax ÓÐ×îСֵ.Éè £¨2£©Ö¤Ã÷£ºµ± a ? ??4e, 0 ? £¬º¯Êý g ( x) µÄ×îСֵΪ
h(a) £¬Çóº¯Êý h(a) µÄÖµÓò. Ç뿼ÉúÔÚµÚ£¨22£©¡¢£¨23£©Á½ÌâÖÐÈÎÑ¡Ò»Ìâ×÷´ð.×¢Ò⣺ֻÄÜ×öËù
Ñ¡¶¨µÄÌâÄ¿.Èç¹û¶à×ö£¬ Ôò°´Ëù×öµÚÒ»¸öÌâÄ¿¼Æ·Ö£¬×÷´ðʱÇëÓà 2B Ǧ±ÊÔÚ´ðÌ⿨ÉϽ«ËùÑ¡ÌâºÅºóµÄ·½¿òÍ¿ºÚ. (22) £¨±¾Ð¡ÌâÂú·Ö 10 ·Ö£©Ñ¡ÐÞ 4 ? 4 £º×ø±êϵÓë²ÎÊý·½³Ì
ÔÚƽÃæÖ±½Ç×ø±êϵ xOy ÖУ¬ÒÔ×ø±êÔµãΪ¼«µã£¬ x ÖáÕý°ëÖáΪ¼«ÖὨÁ¢¼«×ø±êϵ£¬Çú
C ? cos ??? ??Ïß 1 µÄ¼«×ø±ê·½³ÌΪ
??
?
? ??
Q ΪÇúÏß C1 ÉϵĶ¯µã£¬µã P ÔÚÏ߶ΠOQ ÉÏ£¬? ? 2 .ÒÑÖªµã 6 ??
OQ ? OP ? 4 £¬¶¯µã P µÄ¹ì¼£Îª ÇÒÂú×ã C2 £®
C2 µÄÖ±½Ç×ø±ê·½³Ì£» £¨1£© Çó
C 2 ÉÏ£¬Çó¡÷AOB Ãæ»ýµÄ×î´óÖµ£® (2)Éèµã A µÄ¼«×ø±êΪ(2,3)£¬µã B ÔÚÇúÏß
(23) £¨±¾Ð¡ÌâÂú·Ö 10 ·Ö£©Ñ¡ÐÞ 4 ? 5 £º²»µÈʽѡ½²
ÒÑÖªº¯Êý f ? x ? ? x2 ? x ? 1 . £¨1£©Çó²»µÈʽ f ? x ? 2 x µÄ½â¼¯£»
?
?aÔÚ?0, ?? ? ÉϺã³ÉÁ¢£¬Çó £¨2£©Èô¹ØÓÚ x µÄ²»µÈʽ f ( x)?a µÄÈ¡Öµ·¶Î§. 2
xÊýѧÊÔÌ⣨µÚ 4 Ò³¹² 4 Ò³£©