2022年深圳市普通高中高二年级调研考试+数学答案

数学试题参考答案及评分标准 第1页（共10页） "<ä’ÉܲŽíµ9.Ëj gõµw»O–q™ı´Ø¬wˇł z[û¢Ö°ÄłËK ÙÕX>ú]¹<v››šeÆ¡> Ä@¡‹àÎ+¶‡ÚÕ¶ |ýz§¥Ù€ØYðdmółO Bc//µQ•fiŸ¸¼[ÚT f !?…ªi€æ©pê5‡˛1œÆ¶vžP¬WíP’þ¤fl ( ) f x x b = + „'š6"ý°øLu7lJÅð ( ) yfx = yxb = + ln , 0 , ( ) 1 , 0. x x f x x x x    = +    $OWîDQ
¡ošrXþfl”/ y x = 1 y x x = + 1 b =− 1 y x = − ln y x = 1 y x = − 1 y x x = + ( ) yfx = yxb = + ͵®uÏç¼ ží−VPùjä 1 b − yxb = + ln y x = 1 y x x = + ( ) y f x = y x b = + ˇtÄð{"l[{GÁÐU7 qéÂÓgØf˙q‰mŁÓ«õ7W&ffyoÁn‡‹ý`Ñ ¬Ý®cÖ˜ÊV!û†0s x y y x = 1 y x = − O 1 ln y x = 1 (0) y x x x = +  数学试题参考答案及评分标准 第2页（共10页） N›4ˈúÜg‚hIÌ–Í~ Oú˘Ý[ÏI ]¡ç˛˜dŽ«4I¾¾ÒŁåŁ Òçy$,þ˛R¿łî*9øÝ 1 2 a = 2 1 2 a = 3 1 a = − 4 2 a = 5 1 2 a = 6 1 a = − { } n a 202236743 1 aaa  = = = − 1 2 3 2022 1 2 3 ( ) 674 1011 a a a a a a a + + + = + +  = +… 674 1 2 3 2022 1 2 3 ( ) 1 a a a a a a a = = … 1 1 nnn aaa + = − 1 2 2 3 2022 2023 a a a a a a + + + … 1 2 2022 ( 1) ( 1) ( 1) a a a = − + − + − + … 1 2 2022 ( ) 2022 1011 a a a = + + + − = − … ¤$‚WuÞ−ˇ…‘ÒXüÒÅ©Ü;˘¹z¨¥ÂþêSЌܛØØÞ_z½kR(àU ù‰žŁ1k7ú`*fÄ/‹… ˘ÜB4Ÿ˚ÍgCŠ7\0…# 1 1 1 1 sin( ) sin ) ) ( ) ( ( n n k n k n kx kx k x f x k f = = − = = − − −   = 1 1 1 1 1 1 sin ( ) sin( 2 ) sin( ( 2π)= 2π π ( ) ) n n n n k k k n k kx k kx f x x f x k = = = + = + = = +    2 1 ( ) sin sin2 2 x x x f = + 2( ) fx 2π ˜èçz ¶ºº„šAcÕh 2( ) f x [0 π] , ( )( ) 2( ) cos cos2 2cos 1 cos 1 f x x x x x  = + = − + cos [ 1,1] x− cos10 x+  2cos 1 0 x− π 0 3 x   2( ) fx 2cos 1 0 x − π π 3 x   2( ) fx 2 2 (0) (π) 0 f f = = 2 π π 1 2π sin sin 3 3 2 3 f  = +     3 3 4 = 0 π x   2 3 3 0 ( ) 4 f x   π 0 x −  2 3 3 ( ) 0 4 f x −   π π x −  2 3 3 3 3 ( ) 4 4 f x −   2 max 3 3 3 [ ( )] 4 2 f x =  ( ) 3 1 1 sin sin2 sin3 2 3 x x f x x = + + 3 ( ) cos cos2 cos3 f x x x x  = + + π π [ , ] 4 4 x− 2 2 cos [ ,1], cos2 [0 ,1], cos3 [ ,1] 2 2 x x x   − 3 ( ) 0 f x   3( ) f x ¶#t2¸YÃ~ÜÃ/ç¸" 2 − 2 2 1 4 3 x y − = 3 3 12 {6 , 40 , 42 , 256} ； 数学试题参考答案及评分标准 第3页（共10页） ±Àø˘šŽÄ<°ÃÂ:Ânùfi gêh…®è}xw*ÚBŸÊ77»Z5‡qEúÐˢŒ“ÔËÎj@RÕ0ý”}'Õ~C⁄
›þi¿4ƒŁÊÓ+èëòÖ Sªû<pÅkA¨”c¿Æ$ «NÐ\UÞZˇ3˜Mfl0é ‰ò1V”òÎaÍÌvëÊY ü‘J¤vu]²±VN‘ı0Ú r (0,1) r h “×Y£Fûm—>ôi`@z 3 3 1 h r − = 3(1) h r = − 2 2 3 3 3 9 3 ( ) 4 4 V r h r r = = − 2 9 3 ()(23) 4 Vrrr  = − 2 (0,)3 r  ()0 V r   ( ) V r 2 (,1) 3 r  ()0 V r   ( ) V r 2 3 r = V 3 3 ÈÂ?Q1˚›S= V íJ`Ï>Ig–[Pb”(ƒ˙ ›~ƒ¿DÙ,Ó2x½,IX&fiØÉxÿê‹"߬wg^˙Þ0FéY´»³qû´ Ü¿Âç—( 17 n = ‘ ˇ´ˇ–~Łñê¿ÊÇïZ.0ׂŸ'8æö@çË·HÚ‹ (17) 12 B = ()8 B n = ˘}LGŽÓ%¢'˘ôSâf ˛Lê„%õ•úöÕDY3&¡ ()8 B n = n˜L⁄&õd–ži¢ýAıZŸ={6 , 40 , 42 , 256} ˘v»ÓV÷Ł Þ1cŠb[BñH|c⁄å+£u>Пƒ›ÕÅú
#Á™1Y 解：（1）由题意，得 1 1 2 b a = = ， 4 2 16 b a = = ， ¾,ÿ'|´žC'ZZX¿k1 分 设等比数列{ } n b 的公比为r ，则 3 2 16 r  = ，所以 2 r = ， nˆÆ™i˝°óÑF!Y§ðe3 分 所以数列{ } n b 的通项公式为 1 2 2 2 n n n b − =  = ． 6ŽøÌŽ½#ÝàLJèèw5 分 （2）由（1）可知， 2 2 log log 2n n n c b n = = = n + N ． Åè”v@U 6 分 所以 1 1 1 1 1 ( 1) 1 n n c c n n n n + = = − + + ˆ q Þ 0 _ 1 ü Ä A ¦ ; • Ü ¢ Cªcž—'²¯w‚æS2DgE8 分 数学试题参考答案及评分标准 第4页（共10页） 所以 1 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 1 1 n n c c c c c c n n n +       + + + = − + − + + − = −        + +       … … ． 10 分 G]Ñ⁄ZÜ 5 ñÃËfiÉ âfl_³¤³»¢…wØm÷_»AÁ˦ì…Tk<y´Ò ‹´ » 所 cos cos 3 tan a B b A c A + = sin cos sin cos 3sin tan A B B A C A + = ìXÑ¿_ÒR±ý ->)kh A B C ABC △ sin cos sin cos sin( ) sin A B B A A B C + = + = sin3sintan CCA = â ö ¨ 3 ⁄  _ ` V ƒ ½  ? O $ ` (0, π) C sin0 C  3 tan 3 A = (0, π) A π 6 A =   ß – ¦ Ä z … M m ê  ž Ö F é xÝáI;ü˛ûòKZæ º4Ó92›9Û¼L sin sin b A B a = 2 a = 2 3 b = π 6 A = 3 sin 2 B = \¡¿X (0, π) B π 3 B = 2π 3 B = = „ ł ¦ Ð ³ Ÿ é ` y
EÎÚÏùÖ π 3 B = π 2 C = 1 2 3 2 ABC S ab = = △ =29éŠý2nüžH•˜Æó 2π 3 B = π 6 C = 1 sin 3 2 ABC S ab C = = △ òŠ:{˝"ŸOØ ABC △ 3 2 3 ³ 1 U e ‚ › k v E  œ ˚  u  ³ Ÿ—`j¸¾»›«j‡³ÄB 2 2 2 2 cos a b c bc A = + − 2 a = 2 3 b = π 6 A = 2 12 6 4 c c + − = ÑPÇYOòiÓ¬FþD1Ñòy 2 6 8 0 c c − + = 2 c = 4 c = ¾ • ] & Ä Å C ÚMm×>Ð]G»ˆÍ D&$ 2 c = π 6 C A = = 1 sin 3 2 ABC S ab C = = △ ı¼øý`õ…wn“Ë-¾ô„ 4 c = 2 2 2 16 a b c + = = ABC △ 1 2 3 2 ABC S ab = = △ ›  “ ½ ù
‡  ê ¨   ¨  è ê hÎ@8?Ëž©ï¹ÙFVÈ ABC △ 3 2 3 t Ž Ê Y K ¥ ü ‚ ‘ õ ‰ ] ] à È 1EÖ>Ê o{½üš *¤í›Î™zfi0ð'趷 ¨lº¿ŒZå +¡«wpß8€OBCD 2 2 OC = 数学试题参考答案及评分标准 第5页（共10页） 2 3 AC = 2 2 2 2 2 2 2 2 2 2 3 OA OC AC + = + = = （ ）（ ） OAOC ⊥ ABCD ODAB ⊥ AOD OD OAOD ⊥ AO ⊥ OBCD Ï þ J • , U C ç p  \ œ ï w 6 ÷ łB4øŽŠ“]@ª¿R®ˇ AOCD ⊥ ODCD ⊥ CD ⊥ AOD (É »¸ˆ,«µÝ/iú CDOM ⊥ AOD©€Ø4ŒÐ4Ñfic‰ M AD OMAD ⊥ CD AD ， ACD CDADD = OM ⊥ ACD ACOM ⊥ v Î Q g x é q Í fi ø í  Ö ©  „ ¦ « ˇ ç  ¡ … ýüˇQc¨>ˆ£êQ^Æ˛r— OD OB OA x y z 1 2 2 BCCDAB = = = (0,02) A , (0,20) B , (2,0,0) D (1,0,1) M (0,1,1) N (1,0,1) OM = (0,1,1) ON = lv·²Ł3ł)jc»nüØ÷ m = (,) xyz , OMN OM ⊥ m ON ⊥ m 0 OM  = m 0 ON  = m 0 0 + =  + =  x z y z 1 = − z 1 = = x y m (1,1,1) − AO ⊥ OBCD (0,0,1) = n OBCD | | 1 3 |cos , | 3 3   = = = m n m n m n OMN OBCD 3 3 Ÿ’²ßn$Æ'crµ2ñ¬‘V BD M N AD AB MNBD MN  OBCD BD  OBCD MN OBCD OMN OBCD l = fɇJ'¢u/±ËU ~/ MNl lBD OBCD O BD $⁄q¶¥ò¿ÌICcÏ%Œ{TOMN OBCD OD E OBCD E EF l ⊥ F ME MF ME OA ME ⊥ OBCD MFE  OMN OBCD 1 1 2 ME OA = = 2 2 2 2 EF OE = = tan 2 ME MFE EF  = = 3 cos 3 MFE  = A D C B O M N y z x A D C B O M N E F l 数学试题参考答案及评分标准 第6页（共10页） OMN OBCDë}–Ä\feàu~¯¶©ò 3 3 Ï‚öÐýSk±€@ñ£Ræ8hc”Í6%žfi1P83…Ì™ xƒ E = ìEÕ¤1æ 1 F = A 2 F = B 3 F = C 123 FFF = 123 , , FFF A B C A B C 1 2 3 1 ( ) ( ) ( ) 3 P F P F P F = = = 1 (|)0.6 PAF = 2 (|)0.5 PBF = 3 (|)0.2 PCF = £»Ãä−˘˚á@@ã˘ÄÛb 1 1 2 2 3 3 ( ) ( ) ( | ) ( ) ( | ) ( ) ( | ) P E P F P A F P F P B F P F P C F = + + T ¯ ‰ ò · W I e ’ 0  Ç ' « ß Í 1 1 1 13 0.6 0.5 0.2 3 3 3 30 =  +  +  = ©Æ¾Ý˛Òfi(Þ€€iœ¡œÐ X ( 0) ( ) 0.4 P X P A = = = ( 1000) ( ) 0.6 0.5 0.3 P X P AB = = =  = xmèí ( 3000) ( ) 0.6 0.5 0.8 0.24 P X P ABC = = =   = ( 6000) ( ) 0.6 0.5 0.2 0.06 P X P ABC = = =   = Þ$À¦j¬N™¨'bçú X P ¬½à‹ÌO: ( ) 0.4 0 0.3 1000 0.24 3000 0.06 6000 1380 E X = +  +  +  = Y ( 0) ( ) 0.8 P Y P C = = = ( 3000) ( ) 0.2 0.5 0.1 P Y P CB = = =  = £JJ{b…÷éØv:¨8mŒ ( 5000) ( ) 0.2 0.5 0.4 0.04 P Y P CBA = = =   = ( 6000) ( ) 0.2 0.5 0.6 0.06 P Y P CBA = = =   = η¸V Y P ¯ÄŒ„ÉŁ7ÀK»Nr.PE ( ) 0.8 0 0.1 3000 0.04 5000 0.06 6000 860 E Y = +  +  +  = ( ) ( ) E X E Y  数学试题参考答案及评分标准 第7页（共10页） Y (0)()0.5 PYPB = = = ( 2000) ( ) 0.5 0.4 0.2 P Y P BA = = =  = –€5Š~ÞE¬ð−$«‹xq ( 3000) ( ) 0.5 0.6 0.8 0.24 P Y P BAC = = =   = ( 6000) ( ) 0.5 0.6 0.2 0.06 P Y P BAC = = =   = @˙\3 Y P  ? a N × t I 7Bþflƒ¯ePrðàYw ( ) 0.5 0 0.2 2000 0.24 3000 0.06 6000 1480 E Y = +  +  +  = ()() EXEY Y (0)()0.4 PYPA = = = ( 1000) ( ) 0.6 0.8 0.48 P Y P AC = = =  = úù³èê32‰y− 4Kflb ( 4000) ( ) 0.6 0.2 0.5 0.06 P Y P ACB = = =   = ( 6000) ( ) 0.6 0.2 0.5 0.06 P Y P ACB = = =   = ©j Y P 0 : } þ ¸ © ¯ Ë ½ ¥ ø ƒ \ T U 0 : } þ ¸ © ¯ Ë ½ ¥ ø ƒ \ T U ³ ä ; ÷ S ü Ô ³ ®  ® ü > = ¶ ; Åÿñ¶3ZÝ
ßàU ( ) 0.4 0 0.48 1000 0.06 4000 0.06 6000 1080 E Y = +  +  +  = ( ) ( ) E X E Y  éþ±0 ndàÔ°¨:−/-‡ *Èši;?„h—ÊŠmœlÏ›žÿ¾ëI©/Ôó¤êÓ‹Ö æ<愩“ÅCúpåp÷ù`5[‡⁄£d43 s˜Z˘µ2 ﹧~0nÌÁçFhÝ2ûR4 0 , 2 ) M x p （ 2 0 (2 ) 2 p px = 0 2 x = ÷Mà‘sx8)\Í–Ú ‹×7flÇ ¤"Cígł÷flÐ 5 2 2 2 p + = 1 p = ê_÷S˚VÝX5ƒs˛§º* C 2 2 y x = M (2 , 2) Ï˚˘¼+0k³%ØpÈ‚› l l x my n = + 1 1 ( , ) A x y 2 2 ( , ) B x y 2 2 y x x my n  =  = +   x 2 2 2 0 y my n − − = #“ð\˘&„c" ßSÓv>N 1 2 2 y y m + = 1 2 2 y y n = − ˆ ÿ @ ì $ ã P š Õ ^ k ) ÿ h Ü ½œ:˚æÜ−Üvh`Ú—þR 1 1 2 1 1 1 2 2 2 2 2 2 2 MA y y k y x y − − = = = − + − 2 2 2 MB k y = + ˆîà#Y
mÉoà¢ı˧‰Á MA MB ⊥ MA MB 1 − 数学试题参考答案及评分标准 第8页（共10页） 1 2 1 2 1 2 4 4 1 ( 2)( 2) 2( ) 4 MA MB k k y y y y y y  = = = − + + + + + ıuº‘tpc9J˚!AÊl¤ 4 1 244 n m = − − + + 240 m n −+ = OÉ¡łÖþ°´ïŁu:d©⁄¥ l (2)4 xmy = + + (4,2) − ?\úšô … MA MB MAMB ⊥ MA MB 1 − PA PB 2 ( 2) x m y − = − 1 2(2) x y m − = − − 2 2 2 ( 2) y x x m y  =  − = −   ( ) 2 2 4 4 0 y my m − + − = 1 1 (,) Axy 2 2 (,) Bxy 1 2 2 y m + = 1 2 2 y m = − ( )