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O-Net คณิตศาสตร์ 2560

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O-Net คณิตศาสตร์ 2560

  1. 1. v ~ ~ d 111tl1'l11 04 fiWVIftltTVI1 [ ·n1"''1!"~rmfltJ 1oo ) I ~ c!t::t ~ c! ~Hl'U1'UUYl~'t1 18 Q:JJfll'Vf'Ufi 2560 n~n 11.30 - 13.30 cu. '~ q~ 'IJ6.................................•..UliJ~fJil................................... &il'llf1U~U61J............................... 'q v trtllll'Yitr~'U••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••'H~~tr~'U••••••••••••••••••••••••••••••••••••• . ~ tllAfUl'H 1. iM'~t'li'l~t>lJtl~u~~,m~tuvlJ ~'Vlff. ·;h~·;wuu1'Vl1-:~tl~u~t~v1ti''lJnT~~,,ih.~m'l 'Vlfl~tllJ "W.ff. 2557 mh.:~ttl~.:~Tii'fl v • 1 "' <11!1 1!1 1!1 .I "~ 1!1 .I """ d "" " "" 2. 'HUJ'Wl 'Vl'lff"W'VllJtltlt> 'li'ltl ~umunttl~l'l'li'ltl ~umwtmtfl'YIHl'Wfl~l'Jfl'lf'Wfl t'li'1l1'v.:~~t>lJ1flm~fl'lllfl 3. ..1nJfifl~vn uuVinm"W 11~t> ~~mm~ulJlJ'Yifl~t>'lJ 11~v m~fiTt:H·h~t>lJhwt~fl'lllfl ..v v ..'1 "=" v . I""...... • "" ~ .:1 't'ilftf;f!'lJl"~lJH lHU'U~ IJ{JlJVI tY'Yift. tll1VIl!UUt111 VI~U " 1. ,,_hh~mff~~~t~lJi'W'l1V1'lflir'W"ll1~tll'Jfl'l1V1'lf1 2. u~.:~1tlv.:~~muf1nlll'llo.:~~t'li'l~o'lJ ~~t>filruum'l'Vll-:~1irv.. 3. u~'I'Wt)~fll'jru~1~J'W!tlv.:~~mu'W~fllJfffllll t~t!tl'l~fltllJfll'l i'lJt~lfffllll~tJ 4. ~,,ilut1~m11no11111vium w~tfiflf111l1tiYv111mHh~'lJlJm'l'Yiflfft>'lJu~~ ~'Vlff. vem~11if Li:h..~~-n~'Vli-n'tl'l~mumc;J~'tluYl1'lm~f1im~1LL~'l'll1~ ('il~~-fn11~~1"11'W) "n11vl1~1~1'elvf~LLU~~~1'elLtltlLLYif~1'Uvf·m~h'l ,::CJn~1LU'WPI~lin~n.!)~l.J1tl
  2. 2. tl I " Cl<:lu tl J"'fo u u _,. Cl I ... !II UlJlJ'YIYJ(;f6lJUlJ1~Q 'l:::(;f~fll'n61YIN111;llJi')'Y11i'YIHfll'lfttl'U1 tlQlJ'i;T11:::fll'll'lUUl tl I -Q J Q.l ct Q.l QJ Q.l 4 ~I c::l ct Sl u .:t Q.l fiW~ft1(;fYJ'l'U6~Ufll'lUU'l:::YitJ'VUlJ1iUlJfttl'U1u'YI 6 ij1lJlJ1~1!1Ufll'll1UUlU11:::~1'V1Yl ' :, Q.l ct ~ Ji Q.l 'V1~'Vt.! 't111tlJYI'lUtlUtl11Hfll'lfttl'U1'1.1U'nU!1U ~'YI1ifttl'.i1'V 2551 ., ... ...,...... " 0 " ·nua:::l6UY~UtJtJ'YIYII;ltltJ uuunY~I;l6tJ~tJtJt.!lJ 30 11u1 ~1u1u 40 'Utl I ...~6'..!'YI 1 "'Ut) 1-32 "'Ut) 33-40 "'1.1611::: 2.5 fi:::UU'.1 ' ' ' .... "'. .,...., ... " "tl1. l'UUU'V6-t.!1lJI;lfJ11 lli'U'YIU~(;ft)lJ l;l01'.I'YII;ltllJ U11:::116~1;ltltJ lJ'.1111..11 tlUtJtJ'YIYJ(;ftllJ I ..., " ... ' " 0 ~" " ..., cv cv " '.i111;l~Yl'Ut)(;TtllJ'Y16QY11UlJU'Utl~tl'.i::: Yll'Ufl1~6lJ I11)tl~tl~VI'.i ~ tl1JV11l11'U'.i111;l~~'U6(;ft)1J u u 11unJmmu n Y~l;ltlu I , !11!11"'1...., 0 liJ!II 't1~tlUfiYI11tltlfllfltllJ IYI 5. ,dt>(;ftltJm~11 1-H'(;ftlY~n'.i:::Y~1llthV~6ulnuuuunY~(;ftltJ
  3. 3. ~Mi.Yl'lrl 04 fllWVlflli.YVli vVI P1 l1ih 2 . ( -- NIETS "" 0 .:t "" 0 anlbloaournomsiinllwtom {ooMSL.IIllll) lU!i.Yl~YI 18 fJ,_.ill'VfUfi 2560 __.._,__(Nic_, !l'tll 11.30 - 13.30 U. ' ''.:! fHl'Hll 1 uuuthuu s ~-;uat>n &at>n 1 rilfltl'UnlJnnq~ X 1111 I • I I -3 -2 -1 0 3 1. IX I < 2 2. 1-x I< 2 3. Ix-11 < 4 4. Ix+21 > 1 5. IX+ 2 1 = X+ 2 ' a-X·aX + 16-X ·27X 1 2. 0 ... ihh1l1 ilfiltYh1V1111UlU~~.:J'Ulfl a = ('f (')" 2 5 2 + 2 2 1. 9 2. 81 2 4 3. 165 4. 20 4 5. 40
  4. 4. '1M«1'111 04 fiWVIfll«VIi wVI P1 l1Ul 3 , T NIETS cv J -=t cv J anlllloaoornomsiinttwiOlllO (ooMISIIIIW) 1.U«l'l'YI 18 tp.Jill't'fUfi 2560 __,._,__CI'IM<_ !Ttn 11.30 - 13.30 U. "' J ~25J625x6y4 I cv !II ~ 3. U't'f11U !'Yilfl1.J'llfl ~ 1. 25 lxy1JGI 2. 25 xyJG"l 3. 25 xyf; 4. 125 X Iy If; 5. l25 lxlyJG"l 1. x(2x)'~~ 2. 3x(2x)X 3. 9x (2x)X 4. lOxJ)'
  5. 5. l1tll 11.30- 13.30 'U. 5. ill a=1+J5 ill aX - a-X' q I I~ f:ll mn a% -x llflllfll ~ + a 3 1. 1- J5 2. J5 3. 1 + J5 4. 2 + J5 5. 3 + J5 " 6. tht11'1Hil'U1'U'l~~ x, y u~~ z 1~ 9 .U-e:~1~~-e:~,tlihiJu'l1~ ( n)Yn • "1. x = x fJflm'U1'Uiflli'U1fl n 2. ~x+ y = J; + .JY 4. tll X < y U~~ Z < Q U'tl1 X > y z z
  6. 6. l1lll 11.30- 13.30 u • ., I I fJU~l'l1-l'uum1r.~u3JfimnJllltl Sl 0 ov i,Sl .ot .ot Ull11llU1UfJU'l1J.J'YI~'11J.J~UJ ~J.JlO'Yiif~OfJU 1. 15 f.!U 2. 18 f.!U 3. 21 f.!U 4. 24 f.!U 5. 27 'YIU..
  7. 7. 18 A B Dk- 8 ~c 18+IO.J3 I 1. '11'U1tl 2. 18+10(J2+.J3) I '11'U1tl 26+IO.J3 I 3. 'tnnu 26+10../2 I 4. tnnu 26+10(J2+.J3) I 5. '11'U1tl
  8. 8. run 11.30 - 13.30 u. 0 " " 0 0 (fHH'UvH't'l sin A = 0.6 U"~ cos A = 0.8) 1. 8 tiVI 2. 16 tiVI 3. 18 ~VI.. 4. 21 tiVI 5. 24 tiVI
  9. 9. 11.30- 13.30 '"· .. '!II !VI !II Q.l I <!!"" !V.::t c1 tll't1!1VIH't10~'ftfl0ijJ~<tllfl'ft!~U 20 l).JVI1 Uil1VIfl B l~m).JVI1 B i2011. 1. 20-Jj l).JVI1 2. 20(1 + ~) &JJVI1 3. 20(1 + J2) l).JVI1 4. 20(1 + -!3) l).JVI1 5. 60 l).JVI1
  10. 10. .o "lV !fiQ.I ~'!fl I Q.IQ.I!! 11. fll't'ilA~H't'i A, B Utl~ C l1JlAtl'1JlCJJVIfl &J.Jl1JlAlCJJV11HItl~ltlflil'tUY3J'ffflfi U l~tl~ B c C Utl~ A nC =0 1. Ans = snc 2. (AnB)UC = 0 3. (AU B) n C = B 4. A-B = C-B 5. B UC cr. A'
  11. 11. 12. 'tn'h 10 l1'tll 11.30- 13.30 '"· ., ., 1) lrm1uu.Uu JJ. 6 'Jflfl'UlltnhtiJu 2) flU~ll£JJlAU'U lJl·m'Uft~~n-mlUAU'U 1JHtlUft~~fl'l£Jl'U,,jAiJU ll1l't' U U'n'UAetfVI'UtHfl'U .,.., q .., A U'n'UAetfVI'Utl..:J'UfU'l£J'U'U'U JJ. 6 ..ootoot0.1 iSI B U'n'UAetfVI'Utl..:Jfl'U'n'U~fl'l£Jl'UAu'U S U'n'UAetfVI'Utl..:Jfl'U~ll£JJlAU'U ., .v .., v q 0 v c c, v " U'tl1'n..:J'tltl..:J'Utlfl11JJ'nfll't'i'UY'Ii.ltlY'Ifl'tltl.:JVIlJJUN'U.flWU1'U'U - 6tl£JA'tltl1 'U'UtlAYI ~t1,1.l~ 1. u 2. 3. 4. 5.
  12. 12. 13. ilnn.1~111 f(x) = 4- x2 Uil~ g(x) = jx+2j 1. DI = Dg Uil~ RI c Rg 2. n1 nDg = (-oo, oo) Uil~ Rl nRg = [0, 4) 3. fl'ilvJ'U~~ g ,,j~~Ufl'U X 4. fl'll~'U~~ f IV q q VI~Ufl'U X l't'UJ~1l~l~f.Jl 5. fl'll~'U~~ f ~~nun'll~'U~~ g tnu~12~,~rn
  13. 13. ,,s;, 12 rnn 11.30 - 13.30 u. y x+y=I 1. {(x, y) I 1 ::; X ::; 3, X- I < y < }- X } 2. {(x,y) I 1 ::; X ::; 3, X -I ::; y ::; I- X } 3. {(x, y) I 1 < X < 3, 1-X < y ::; X -I } 4. {(x,y) I 1 < X ::; 3, I- X ::; y < X -I } 5. {(x,y) I 1 < X ::; 3, 1-X ::; y ::; X -I }
  14. 14. •tn~l 13 rnn 11.30 - 13.30 u. .. 15. ft1'11t~~t1u11J~hfl'~ 1oo vt~..l &ilu~~il 1 , 2 , 4 , 7 , II , 16 , • . . , a50 , • • • , a100 I !V olct c1 I I 't U"1'n~ti'YI 50 ( a50 ) J.Jfll&'Yil&~ 1. 1,176 2. 1,226 3. 1,276 4. 1,300 5. 1,301 'j~f.I~'Yil~ 20 ill"').J~'j 1. 28o nl"').J~'j 2. 64o nl"').J~'j 3. 98o nl"').J~'j 4. I,280 nl"&3J~1 5. 2,s6o nl",,..~'j
  15. 15. 17. fX1 A = { 1, 2, 3, ... , 10 } B = { 4, 8, 12, 16, 20} Utl~ C = {xi (x+1)(x-4) = 0} 2. B UC = B 3. A nB = {4, 8 } 4. B- A={12,16,20} 5. (An C) U B = {8, 12, 16, 20}
  16. 16. 't1ih 15 rnn 11.30 - 13.30 u.
  17. 17. run 11.30 - 13.30 '"· ." " ct !'I I 19. t~unnmn'Utl~VIl'U'Utl~~u.JA'I11UJ).J3j).J'l'lln Au'U x, x +2 ua~ x +3 '11'U1tl X 8+3/6 I l. '11'U1tl 8-3/6 I 2. '11'U1tl 1+/6 I 3. '11'U1tl 1-/6 I 4. '11'U1tl 5. 11 + 6/6 11u·;m
  18. 18. n'tn 11.30 - 13.30 u. 0--------------------Q X y 1. V = 2x2 (2-x) 2. V = 2x2 (3-x) 3. V = 2x2 (4-x) 4. V = 4x(2-x)2 5. V = 4x(3 - x)2
  19. 19. '11ih 18 n~n 11.30- 13.30 u. 21. y X 0 2 3 2x 2 - 4x+ 3 > 0 0 ... 1. 'tJfHll!1!'iJ".i.:i X cS I 4 2. Y! = Y2 flfltln.Jt:l 4!1 X = 0 '11".Jt) X = 2 ' 3. Y! <Y2 cS I 4!1 flflt:ll3.Jt:l 0 < X < 2 Q.l _J ( )2 I ; I -·· 4. <tJV11flflt1'U,t:l~fl".iln y1 = 2 x - 1 + I t:~gfllfl1lfl".iln y2 = 3
  20. 20. A.l 0 X ( ) <!I I Gl !II 'I 22. 'lllflfl".ilTt lCUVIfllVI61J'16~el'tl3Jfll".i - ~ X 4- X fl6'tf1~ I'U'Itl&Vl 2 y 1. [0, 2] 2. [0, 2.5] 3. [0, 3] 4. [0,3.5] s. [0, 4] 1. 5 2. 9 3. -7 4. -9 5. -58
  21. 21. l'lih 20 run 11.30-13.30 u. I !II cvc:t o "''II c:t '!fiCV 24. ~lnl'Hl~A"lfJ~mU1UA~).J&UU~1'YI 1, 2, 3, ... (mO'lJUt'l~t'IH) AuU~~.fll'Vt 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1. 60,025 2. 62,525 3. 65,025 4. 66,225 5. 66,275
  22. 22. R = 5e-k + 5e-2k + ... + 5e-nkn I I .!! ~I I "" llltl k ~~~~ e luUfllfl~'t11.Jlfl I .. I 't1ul 21 n~1 11.30 - 13.30 u. u~·nAt~lnunfifl~agiu1HmtJ rlaum~111mfl1~fi 8 &iJurrh1V~ (il~an1t~) 5. 5e-k [l-e~ 8 :) 1-e
  23. 23. run 11.30- 13.30 u. + V lJIV '""' 75 tl~U'U'U Ul Ufl'U &Vltl~U'U'UUfl1Jlllflfl'Jl~'J 25 fi~U'U'U 1. 6.92 tl~U'U'U 2. 12.50 fi~U'U'U 3. 77.50 tl~U'U'U 4. 82.50 fi~U'U'U 5. 141.00 tl~U'U'U
  24. 24. " ' " " " fl-l-!1 l~U.IA~lfhA~~tuileuflW~eu~-!!fl~&nn..!tJ~'Un-!1 3 fl-l-!1 U'U'Uth-!!'lht'illfl~-uJ ., 0 Q.l 0 Q.l 'IHt'i'Ufl w1 , w2 Uil~ W:3 ~UJill~'U , J ~ = W;.. £ j ' i =1,2, 3 wl + w2 + w3 3 fl =0.1 5 ' p2 =0.25 Uil~ IP; =1 i=l ' ., .,V I .o::l .,. I o u <V .o::1 .::1.::1 I Uil1fllA~iltiAileuflw~eu~-!!fl~UtttttJ~'UU'U'U tt1-!!ttl't'ittfleu~-!!ttm-,tlttfltttt3Jfll 1. 68.3 fl~UU'U 2. 70.7 fl~UU'U 3. 72.0 fl~U'I-.!'1-.! 4. 73.7 fl~UU'I-.! 5. 74.5 fl~UU'U
  25. 25. ntn 11.30 - 13.30 u. 1. 15 2. 18 3. 19 4. 20 5. 24
  26. 26. run 11.30 - 13.30 u. 29. ll1,;1.:J (x-3s,x+3s) n-hfl'u (1400, 1580) 1. X 1445 Utl~ s2 = 2025 2. X 1445 Utl~ s2 = 45 3. X 1490 Utl~ s2 = 45 4. X = 1490 Utl~ s2 = 2025 5. X 900
  27. 27. ,;;, 26 rnn 11.30 - 13.30 u. ""1~m:rnn (Ul'YI) 3 4 5 6 7 8 0 " 'illU1U')flfll (tlU) 8 5 3 2 1 1 'I c:t "" I '1.1 c:t '1.1 I v c:t 1. flli'1HUJl'ileutlWVI I'YilfltJ 4.3 Ul'YI ).Jfitl!lU I'YilfltJ 4. Ul'YI "" I .., "" ~I " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ IUUfll"lfl"l~'illtJUtJtJitJ'YIHeu11 '' .ct Q tcv .ct v tu q 2. flll'1ltltlltleutlWVII'YilfltJ 4.3 Ul'YI ).Jfitl! lU I'YilfltJ 4 Ul'YI 'I c:t "" I '1.1 c:t '1.1 I '1.1 c:t 3. flll'1ltltlltleutlWVII'YilfltJ 4.3 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI "" I .., "" ~I " " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ IUUfll"lfl"l~'illtllltJtJitJ'Yil-!ICUltl 'I c:t "" I '1.1 c:t '1.1 I '1.1 c:t 4. tlll'1ltltlltleutlWVII'YilfltJ 4 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI ', q Q tcv ..r:t v tQ.I .c:t 5. tlll'1ltltlltleutlWVII'YilfltJ 4 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI "" I .., "" ~I " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ luUfll"lfl"l~'illtiUtJtJitJ'Yil.:Jeu11
  28. 28. run 11.30 - 13.30 u. I ., ., nm1uw~:00fl i11 2 1"1-r~ ur,: 00£1 2 1"1-r~ l't'hn1Jifh1~u 1. 2 2. 3 3. 4 4. 5 5. 6 32. 25 20 , '"""" r! Utl: 3-JJJ~fl'ltll'Uti'U~ rrhn1Jifh1~ 1. 1 2. 2 7 7 3. 3 4. 5 7 7 5. 6 7
  29. 29. run 11.30- 13.30 u. . . 33. ihttu~un11lt1u ABCD utr~-:J~,:jlU 1~uii~l'U AD tin 15J2 'tnhu u~1 V 4 I ~l'U AB tll1fl11'U1tl B D C 34. 2-JS ' 4-J9' 8-Jl3 ' 16-ffi ' ...
  30. 30. - tttttl~~~ltlU·¥~t-~~tttttl~M.flie,X-X9-9If1tll~~X1t!.6itttttl~'L/i trJ~iM..I(,L@NJM.U.tJUQitlA.ttlMl.QtYU~It"t-lA.Ittim """""""""""""'"""'"""' IIA ttYfl.QtY9tl1~iHI1QlttllA. ~~'0 ttYfl.QtYOZt~.l!t-lllU~l!Uttt.l!llA. "';o"'""0 .. ttYfl.QtY£Zth).l!t-lll!i~l!ULttllA. "'I'"'""0 .. ttYfl.QtY8ttt.l!LU.~l!UlttllA. "'00 ttYfl.QtY0£ttt.l!llA.ttYfl.QtYv£lttllA.LO l"b0l'b0" t~.l!t-lll!iQt"ttt.l!LU.lttllA.M..I(,L@ItlA.ttYfl.QtY09ltt-tt"t-"Uttlfl.tc"'9£ I'no""1r'oo""""""no""5:71IT)1 10II t~tti~ttJ~.:~mt-.1aL.l!i~~Deu.tth)L.l!ttl!n .,.""""I"""'"' II h)~YR.l!tn.~l~tfl1(Hl.l!i~l!UVL.l!ilttt)tt~UiA.L.l!it-QR.t-.1ttltYfl.~l~ ~nnth)rtih)M.Jl:li~zttUH"DettU~h)Deu.n~~l!~Ul.l!it-QR.Hl!UttunU.ll~! """>II"'""I""ITiI"" II t-t~tt.l!ttnnnwaLDI~nnvL.l!it-Lt"~tttM.iLDmntLUt-Q~lllt~rtth)ttJl:ltooz JTi(,I~hvJTiJTi.,. ttUH"Det-~~nnt~rti~M.Jl:li00£t-.1gL.nit~rti~M.Jl:liOOIt-.1Vl.l!t'S£ l'b'•l'bb':::7 .. ·n0£'£1-O£'JJ ..--.-S.l3fN~;o"'f"'~'"' Lntt~=~->·==~09Slmru.twtt~81IULDntt 6Zlef(A,b1f~Dll~~~y170LJlotDAtt ltt" "'
  31. 31. run 11.30- 13.30 l.!• ., 39. tl c:l <Vc:l 0 fl:::Ul.!l.!'tHl1.J 'i:lltlillfli"WWUtl.:Jl.!fU"Wl.! ~ll.!ll.! 25 fll.! aiJcu~~9ltl,tJil 60 65 65 67 70 71 73 75 76 76 79 81 83 84 85 85 88 89 90 92 95 96 99 100 100 ' ', v iJ tl r! " , r!c:l '11 P25 I l.!l tl'Wifl.! 'Yit'I'YI 25 &It'!::: iJ tl r! " , r!c:l P75 I l.!l tl"Wifl.! 'Yit'I'YI 75 v <::11 ·~ mn P7s - P2s 3Jflli'Yil ~

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