ข้อสอบโอเน็ตคณิตศาสตร์ ม.3 ปีการศึกษา 2559 พร้อมเฉลยจาก สทศ.

1. I
v ce:t v c
~Hl'U1lU~l1'YI 4 fUJill'VfUti 2560q
t1'tll 09.00- 10.30 'I.A.
I
~ q~
'lff>•••••••••••••••••••••••••••••••••••,l..j1'-Jil'fJil..........................•..••.... til,tl'lJ.!JU'f)1J...............•••..•..•.......
I
q v
fl't;"J1Utlll'61J.............•......•...............................................•...'t1'0.:j'£1'tJ1J•••••••••••••••••••••••••••••••••••••
0 ~
tlllflt>H
1. 1,r~',h~vulli]u~~1lJ"J:;1iivu ~nft . 11~-;wm.nnl.:Jui]u~&riv1numHhrih.Jm"J
'Vl~~VlJ ~ .ft. 2557 VV1-:J1fli.:Jfli'~
v o 1 Ql .- <!! <!! <!! -I .-~ <!! -I "'"" d "" .- ""
2. 'l1UJ'W1 'Vl'Jft~'VllJvt'IV '11'JV ~1JmtlH1V~1'J '11'JV ~1JmWVH'lf1'Vl'JV'Wf1~'tJf1'tf'W~
!J/ !J/ 1 d
1'J1'11V.:J~VU ~W1~~'J1~
3. 11'1lJf1~nlvn u'Wnnm~ 11~v 1~mmiuuun~~vu 11~v m:;~nllt'h~vu1~m~fl'll1fl
.."' "' }I ~ " - ~ ~ ~ o ~ u q
'l11fl~1'llltf8lJJ>·oll~U'll8Uol)lJYI tfflt'l. 81l~11U'Ufl11 ~.:Ill
"1. ,tJtJ"J~tllft~~~VlJi'W"J1Vi'tf1'1!'1.J""] '11~8 lJm1Vi'lf1
2. U~.:J'1tJu.:J~tll'Wffflll1'JV.:J~1,j'1~VlJ 1~V~hU'Wf11'J'Vl1-:Ji'l!v
3. u~n'lq~m"Jru~iN'W'1tlu.:J~mu'Wm"Jffflll1 1~vtl"J~nvum"Ji'u&'li'lfff1ll19lv
4. ~11U'Wfl~mlJf1t)'11lJ1Vi'WmW~1fl~fl11lJ1-ffV'I11VUfh~ulJtll'J'Vlfi~VUU~:; 'ff'Yift.
1VfH1'1'j if11'J'W~'llifnf'llV.:)~tllU'W'Y1fl'ffVU'YI1.:) f11'j fffllllUli.:!'lfl~ (v.:~fi'fll'j lJltl'lf'W)
"m"J .YhCJ1111~v~flu11~.:J'I1~m~vu~1.:J1.l~.:~n~11 'il~1n1i1ru'Wfl~~llJf1t)'11lJ1V

2. .. .."' .... <!!
f)l~ftf)'U1'1J'Urt'Ug 1'1-A ft.ft. 2551
"
11f.l"::&tlf.I€1U'I.J'I.J'mUnm U'I.J'I.J't1€11TO'I.JilU'I.JUii 21 '11~1 'l1u1u 30 'lio.
'
VIO'Un 2 'lio":: 4 tl::uuu
.. '"'<:1<:1 ,~~~~ o Slcv cl ~l" Sl
3. U'I.J'I.J't1€11Tfl'I.J1'lf1'UtJ'I1"1f.l1€1 '11 &'11€1l11'0€11 2B ~::'I.Jlf.J1-3f)"tJ'I1'U1YI11tl'IJ't111J'U~'t'll1'1€1'1Jfll'l'fl'I.J
'~11/ 0 ~SI Sl VQ.I Q.l Sl Sl..,l
't10g€11U'I.JU'UO-!im ~ €1l'l:lfiWIO'I.J &'t'IJfWIO-!iVI'a-!if)'I.JVI11tl'U'a'l1tl'1Vl'UOtl'O'iJ'iJU't'IU1uf)
UUU't1Vltl'OU
' 0 0...... " """" " " " , ..; .. "~ ....4. 01'Ufi1U'U::'U11titnl YIO'I.J'IJOl'I'O'I.J &'111'111 &<ij Utl1YIO'I.J'IJ011'fl'I.J€11f.JVI'Uifl-3Utl:: tJ!flfl&'t'lfjO'Utl€1tlflf)
fl1Yifl'I.J,~
~ .. 1" 0 :wt!'l
5. &tJouou&u~ '1 '111Ttl€lnl::€11'Ufi1Yitl'U n &'UU'U'U't1€1trou

3. ., .
v.-r~~nuhrl'u;i,..iifhn.i 1ufi 1 ~fl'llfl~ 2560
...., <:1
1. 1'U'YI 12 ~fl'llfl~ 2560
...., <:1
2. 1'U'YI 20 ~fl'llfi3J 2560
...., <:1 <:1
3. 1'U'YI 1 ~'Ulfl~ 2560
...., <:1 <:1
4. 1'U'YI 2 3J'Ulfl~ 2560

4. 't'i'l
9
ll 3
rnn 09.00 - 10.30 u.
0 <S ..; 91 .,; ' <V rl 1 2
2. linU1U&VI'-J'YIU~r.J'Yii!Vl Ull~'-Jlflfl11Nilll'W1i'U~.:J 3- X 5- + 2.5 + 6.25
3 5
1. 3
2. 4
3. 18
4. 19
91 m n 2123. ~1 2 X2 =
m n
26 91
2 +2 = Ull1
mXn rrhi1urrh1VI
1. 2
2. 24
3. 27
4. 36

5. -
t~rtUM1.JMf:'ltl~O~I
...·~
t~rtt~tt.Jbtt-ltl~Zfl'£ ...
t~rtt~tt.Jbtf:'ltl~9ll ...·z
t~rtt~tt.Jbtt-ltl~OZI'I
~ttu.t~rtM.r:-u.tt:tu.tu.trt~~t~m~nJbtorr:-1rtJb~L~
I';:""f"!(5:>""5:>~
t~rtt~rtJbts~~n~'£nntrtL~tlrJrtLtlJrtu.rtrmM.trtL.L!ntnnmtirtrtJbtrt·s ""lsi~""""""I~lsi""s:>bl• II
t~ttt~rtJbtLZ~~rtYtttttli'JU.rtl~f:'G.L'!rt·~
...~Ill,""~"" I
t~rtt~rtJbtSrtYH~tli'JU.rtl~f:'G.L'!rt'£
"""'I5:>~5:> I
b
t~rtt~ttJbt9ItW~.L'!U.tLrJU.ttL~·z
~~~~
t~rtt~ttJbtstwr:-nM.nL~rt·r ...5:>~"" I
r:-a~u&ttmG~~LGn. ~5:>J~IItI~
..
t~nt~ttt~ttJbt9£ntn.aturJrtLtlJttttrtrJ~"'"'L.L!ntt~ ~...I~"""""",~~ ,.I
.... s:~:£nntrtl.L'!t-U.rtl~t-Gn.twrtLtlJt-Gn.rtt.L!Lt~Grtt-ttM.rttrtrJ~M.mL.L!rtt·~
lsi,~I,""5:>I~""I~
..II
·nOf'OI-00'60L~tt
..S.l3fNiit'SI',!"'',
~':!,~;===•.09SZ!lrtMLlfrtU~U.tl.L!trtt
tlrtM.~
ld(,1,a!f~.L'!l"~~IJt6LJlot.L'!,ltt

6. ' ' .. ., ..<:1
"" <:1 <:1 .c!l
" " "" "" ""6. 'V'fl~ 3-JVI!11HITI1tUJJ.JN'UNl fl1H 6 'U1 Ul1 8 'U1 Uil~ f-:.1 10 'U1
..<:1 ... <:I elm ,~
fi'j~J.JVI'UJ.J 'j3Jlfl'jn11 VI
1. 120
.,....]fl1Jlftfl'U1
2. 160 -~]fl1Jlftfl'U1
3. 240 -~1fl1Jlftfl'U1
4. 480
.,
"""]fl1Jlftfll1
..<:loJ) t <S tV .., <S t"" <:1
3-J'Ul A'l1ilNl'U&VIJ.J't16V11UtlVI'jl&'j1 2.5 &3JVI'jfltl1'Ul't1
•1. 300 ]fl1Jlftfl&J.JVI"l
•2. 1,800 1fl1Jlftfl&J.JVI"l
•3. 18,000 ]flUlftfl&lJVI'j
•4. 180,000 ]fl1Jlftfl&lJVI1

7. 8. A E B
~--------~--~
F
., . ' '
V V <!I <:t _l <:t <:t !fl I '
til BF = FC U"~ AE = 4EB U"1 'nl.!'Yil1Jtll't'i"tl~ BFDE llJl.!!'YilA~
1. 7
..
2. 1o ~n:n~ih
..
""3. 13 V111Hl.!1
.. ..
tll1 7 ICJfl.!~I~VI'l &9l~th{lt.!l~~tl1tl'n6~{l~,~'lhlfi~lVI'll't'h1~
0 "v 22
(fll't'il.!~A't'i 1t = -)
7
.!
""1. 88 }flUlftfUCJft!VII~VI'l
.!
""2. 154 }fl1JlftfUCJft!VIl~VI1
.!
""3. 462 }flUlftfUCJft!VII~VI'l
4. .! ""
616 }fl1JlftfUCJft!VII~VI1

8. t
..., .! Q,
1l!Ull'rt1 4
flWVIf1UYVJi ~~VJ fl1( _c NIETS
.Jt~ 1 t!
2560 ar!Uimaoornomslblwiom (oownsui!W)
fJlJ.fll Jt 1111i --<1-T--O'IMo-
0 ~!II 22(fll't'il!~ '11 1t = -)
7
1. 280 Vll'H~UlJVI 'j
2. 440 VJl'jHilJVI'j
3. 594 VJl'jHilJVI'j
4. 880 Vll'jHilJVl'j
l1t'11 09.00- 10.30 '1-!.

9. -
u&Llan.u&n.an.~Nuan.·p
"""""
u&Llan.~Nn.an.u&uan."£
"""""
~HLlan.u&n.an.u&uan.·z
""'"""
u&Llan.u&n.an.u&uan.·r
"""
t-~~tt(ll~tGl'ot1.~~t-Q.QMll!UUf.Ll!>Mo
lttl-tttl~Mll!LlHll.ttl~M.ll!n.ttn.ttl~M.ll!u
"""""
U.t-~~t~ttl-tl~~~~l1l.Q
~I
IJWUYlll.tlntt-Qil.lttl-tttl~~l!llHll.ttl~ttrtttl~t-QI1tlUUL~~~U.IJI1t'Q.QMll!~Y~~
""'.-""""""~""'""'"Ill I
~
:
//tl
.·.
tl/
~L~~ttL.l!IJ~L&Ln.t~rtt~ttH.L~·u
•tt0£"01-00"60ll!tl__,__,_,___09SZ!ltt.Mllfi1UJ7U.tl.Qittt
(~)!!IJIO!-fii.VSilJOI.UilCilOIJ1UII~p"'t:>pno
S..L31N~I
8l~l-tw(,1,fafiJ.l!LWIJ~LlJ76Ut.t.l!,ltt

10. / / /
l.l
/ /
l.l
/
'... ... 0 .. -=~~ " " " <!I "
ftl'l'HHl-3lJVIU"'VI-3'll'U1Ugfl1JUHl'YI &VI'llflfll'.ilJtl-3 Vll'U"Ul-3 'H'.itl Vll'U1JU
'Utl-3llJI'.i'UlflWVI"'llJij~ flt>"1Yt>1VI
-3
2
" "2. ftl'nVIl'U'UH 2" "1. ftl'nVIl'U'Ul 2
1 2 1
"3. ill'WV11U1JU "4. ill'WV1l'U1JU2 1
2
1 2
2

11. A
13.
c
i1 A 0 il
m BDC = 120 mn
1. AB = AC
2. BD =CD
A A
3. DBC = DCB = 30°
A A o
4. ADB = ADC = 110

12. 14.
A
5 D
. .
An l_ BC fl"l71 D U'il~ BD un 5 't1t.hml'~1 DC fJ11fl't1hrJ
I
1. 8 't1'.!1fJ
I
2. 9 't1'.!1fJ
I
3. 12 't1'.!1fJ
I
4. 14 't1'.!1fJ

13. 15.
l'y
"'A
"'L . ...
' -0 X
1 B
"
..
1'l'lt.l A IU'Wlt.l~uuuu tn1ut.lt1.:~1w~tJ1~fitJ,t.lil,3.ilh1'l',o~ illvt B
1. 't'i~'Wltl~tAuuu 1tl'U'll~ o 1"Wllfl't1H't11'W!aUa.J'WlWtniU'U~a.J 180 tl.:Jfll
!II -·!II ~ ct ~· !II !II !II !II ~ ~ ct
2. t1'~'t1tl'U11JVI'UU'U'U &~Ua.JUfl'U Y !lJ'Uitl'Utl'~ 'tltl'U Ut11tl'~'t1tl'Uillvt't1&~&~UlJ
..
'
3. "~ntJtA1t.l~tA~mul~uiluntA x IU'WI~'W"~ntJ'W u~1t1'~ntJ'Willl1nM1~uil..
' '~ -· !II , _ . !II ' !II !II ct'IJI ~ ct
4. !tltl'UllJVI'UU'U'U'UUl'UUflU X lJ'tlHCJflrJ 6 't'i'U1U Ut11tl'~'t1tl'Uilll1't1l~ &~UJ.J
UflU X IU'UI~'Utl'~lltl'U

14. 16.
rnn 09.00- 10.30 u.
D
A
I I
• "l" _I q " v -1 q
fll't'IUV'U't'i "hJil'UU't'i"tUJ3J ABC flilltlf11J1IJ!l'l3Jl't'iiUJ3J DEFv v
lUil'l3Jl't'i~t13J ABC il~1Ut111 2 ~1 3 ~1 Uil~ 4 ~1 Uil~l!Jil'l3Jl't'i~t13J DEF
ilfi113Jtll11~1Jl11 36 ~1
I V
q , qq ' Q.l ~
3. 3Jil'~.:JV11U't13Jf1113Jtll1~l.:Jf1U 20 U1

15. rnn 09.00 - 10.30 l.!.
0
17. fll11l.!~
4' 7' 10, 13, 16, 19, ...
tthmuulU"U~.!i.Ull.!1l.! 1vuJ
clct
1 IU't..! 4'VHll.!'t1
clct iJ
vn1l.!n 2 1 u 7
clct iJ
'W1ll.!'t1 3 I l.! 10
'cl.q iJ
'W1ll.!'t1 4 I l.! 13 .•.
.,
V ~ I ~tJ l:f., I V
'U~ vwm l.!_Mgtwm.!i
'
1.
cl.:t
'W1ll.!'t1 1s tiJl.! 54
clct
1s tiJl.! 462. 'W1lt!'t1
' V I clctcl.q I
3. 'W1ll.!'t1 17 l.!~tlfl1l'W1ll.!'t1 19 ~~ 6
clct '<V cl.:t I <V
4. 'W1ll.!'t1 10 11a.Jfl1J'W1ll.!'t1 11 A't1lfl1J 65

16. I
( A'lf'l-l 12,13,14)
.,
tl1Ntl"l13H11Q"U6~1Jfl"liJ~tT13JfiUAcy),OUfl1Q"Ufl~~~tlll'lf1fl't'ffl~ 1Jfl"lflU1flfl1QAcyj,1~
1. 22 iJ
2. 23 iJ
3. 24 iJ
4. 25 iJ
il
1. 14 ~13.1
il
2. 33 ~13.1
il
3. 34 ~13.1
il
4. 35 ~13.1

17. !II
't'I'Ul 16
1. X -1
2. y = 2
3. y 3x-1
4. y = 3x + 5
..0 Q.l ' Q.l
1. tHH'lll'U1U'U'U(;)HflU 16
..
2. Nt1t]W'Ue>~tfe>~111U1UUUIUU 18
3. 't'l~~1utJe>~111U1U,i'UIUU111U1U~
. ..
4. 't'lcU~1utJe>~111U1UUU3Jlflflll 18

18. run 09.00- 10.30 u.
22. il iJ 0
til (a , b) A 'Ufi1VIfl1.J"llfl~".i~1.J1.JtUJtn".i
3x + 6y = 0
3x- 2y = -8
il iJ 0 1 il~mn (a , b) ~~~ 'UfllVIf>U"llf>~trlJtn".i 'U"llf> VI
1. x+2y = -3
2. x-2y = -4
3. 2x+y 3
4. 2x-y = 5
.,
cv<:l "" !'I i/o cv cv<:l "" ~~
".i1lJ"llf>~UfU".if.l'U'Hty~'t'Jflfl'UAU'U 4 : 3 tll'Ul'l1Ufl'l1lJ"llf)~l,!fU".if.l'U'Hty~fJflfl'UAU'U
1,050 nltm1lJ Uil~Jl'l1Umtl~f.l"llf)~Um1£Ju'trlf.l..rf)f.lfl';h 70 nl~m1lJ~~iium1vu
1. 12 fl'U
2. 16 fl'U
3. 20 fl'U
4. 21 fl'U

19. -
IZ
Z1
oz
[[
ZI
L
L
z
•t
"£
·z
·r
~ill.Utt,n.y~tUItU!~~l:m
blIJ>,."~
~ttlIt-QIUU~~ltUU!i~trT.fl!.t~lH!UM,U.ttt.n.Y~~UtrtltiR~UtturtQtMlrtUQQ~rtiZ
,.1;7~"Ill"'"'!"IJ>I",",.
~Ltuulin.nr.trth~u~MLO~tu£rt~.Q~~n~rtitt-G~r.tm~Ltuulirtr:-tt.&-~,n.wt-i'1·sz
"'1"'",."""',.1;7""""r"
tt.ttt.l~81•t 0
tt.ttt.l~Z1"£ 0
tt.ttt.l!;OI·z
tt.ttt.L!;9·r
tt.ttt.l!;!~rt!.tt-_lt~LOOtl~UilG,tt~nOO'Zl~UUlrttt._tttt.ttt.l!;l!ll~l
.,.,..
tt.,Yl~ftL~~ln.~Yt!U~!.t~~~nY~!.trtl~tt.ttt.l!;tt.(lit-ll~.flrt~~ln.~it~,(tlt
..
~~~~
tt.t-~n.Lt~~1n.~r.t~n.rt·tz ~,,~
..
•tt.0£"01-00"60L~ti--.o--i-,.--~09S'Z!ltt.MllfrtYtUtl~itt.t (lliiUIIISt~)QIIIO~qsUOlUflCIIOm!lll.lll~i',J;>I',
SJ..31N~'
81l~l-1,wIA,fa}~.Ql~~~y1:'6U(,ti~~t

20. ' '
~tJufi 2 uuu'j~tJlt~~·;ut11JnAiJutih~tJu 'l11u1u s ~t)
~----- b -----~

21. 28.

22. 30.
il I <'!! ..., .q il ~ -• !SI I !SI ..d IJ il
f:lli;p.Ht1tlfl".i·Uf 2 &il''U&'ntliJ".i~fltl'UhJ'U~tJ tl'llti'Ul'll~&u'U'YI'll~ &~~tJU'tttltl
&iJun·h1~ (~tJu1ulU'Yitl'UtJ3J )