! "#$%&'(') Môn thi: TOÁN $*+,+ /0#10+234$56 (không kể thời gian giao đề) Bài 1: (2,0 điểm) $71+896$:&2 ; ' ; ; ' < ; ; ( ; = ; ' + − − = − − − − − + >?@+;≥?0;≠AB C 56,%.1+896$:&<C 'C D#,+E6FG&H-;I8 < = = C Bài 2: (2,5 điểm) $7$J4$KL.,6FD.$2 ; M # ; #M + = − + = − >#/06$-#NOB C +P+$J?@+#QR' 'C D#&E&,+E6FG&H-#I8$J&S.,$+J#T9M.$U6>;VMB6$7P#W.MQ; ' Bài 3: (1,5 điểm) F7.,$J67XIY;MZ&$7IK*.,6$[.,>TB2MQ;\'?0-F-17/>B2MQ; ' C ]E&IG.$67XIY$-+,+-7I+8#^?0&H->TB?@+>B 'C $7I+8#_6$9Y&>B&S$70.$IY/0#>?@+≤#≤'BC_2 _^ ≤ ') ` Bài 4: (3,5 điểm) $7IK*.,6Fa.6b#ZIK*.,cd.$^Q'C%+/06F9.,I+8#&H-^C<9-ce TbM?9f.,,S&?@+^C C $:.,#+.$2 -B :,+E&^/0$D.$6$7+C 1B · · ^ ' = C 'C $:.,#+.$Fg.,/06Fh&6b#&H-∆C =C ]E&IG.$?G6FdI+8#_6Fi.&9.,.$jI86k.,>_\_\_BIX6,+E6FG/@. .$U6C Bài 5: (0,5 điểm) +P+1U64$KL.,6FD.$2 = ; R =R ; l; '; ; + + ≥ + RRRmRRR H v tên th sinh: ………………………………………… S" b$o danh: …………………… Gi$m th' 1: ……………………………… Gi$m th' 2: ………………………………………… HƯỚNG DẪN GIẢI Bài 1: (2,0 điểm) C n@+;≥Z;≠A6$D2 < ; ' ; ; ' > ; 'B> ; =B ; = ; ' + − − = − − + − − + ; ' ; > ; 'B> ; 'B > ; =B > ; 'B> ; =B + − − − + − − = + − ; ' ; ; l ; = > ; 'B> ; =B + − − + − + = + − ; = > ; 'B> ; =B − = + − ; ' = + noM < ; ' = + >;≥Z;≠AB 'C n@+I+p9c+J.;≥Z;≠A6$D2 < = = ⇔ = ; ' = + ⇔ ; ' =+ = ⇔ ; = ⇔;Q>6q#BC noM?@+;Q6$D < = = C Bài 2: (2,5 điểm) C n@+#QR'Z$JIW&$76Fr6$0.$2 ; M ' ; 'M + = − = − ⇔ ; M ' =M = + = = ⇔ ; M = = C noM?@+#QR'6$D$JIW&$7&S.,$+J#T9M.$U6>;VMBQ>VBC 'C J4$KL.,6FD.$IW&$76KL.,IKL.,?@+2 ; M # ># BM # + = − − = − >sB JIW&$7&S.,$+J#T9M.$U6c$+?0&$tc$+$J>sB&S.,$+J#T9M.$U6C+p9.0M;PM F-c$+?0&$tc$+#≠⇔#≠C$+IS.,$+J#T9M.$U6&H-$J>sB/02 ;QR#ZMQC $u7,+P6$+v6MQ; ' Z6-&S2Q>R#B ' ⇔#>#\'BQ⇔#Q$7w&#QR'C v6$x4?@+I+p9c+J.&H-#6$D&S$-+,+E6FG&H-#&y.6D#/0#∈zVR'{C Bài 3: (1,5 điểm) C 70.$IY,+-7I+8#&H->TB?0>B/0.,$+J#&H-4$KL.,6FD.$2 ; ' Q;\'⇔; ' ;'Q nD-1\&Q\'Q.i.4$KL.,6FD.$6Fi.&S$-+.,$+J#; QRZ; ' Q'C |ISZ67XIY$-+,+-7I+8#&H->TB?0>B/y./Kx6/02^>RVB?0>'VlBC 'C -F-17/>B?0IK*.,6$[.,>TBIKx&?}.$K $D.$C nD_6$9Y&>B.i.67XIY&H-_>#V# ' B %+ZZ/y./Kx6/0&$b.IK*.,?9f.,,S& $X6|^Z_Z;9O.,;C $+IS>RVBZ>#VB?0>'VBC 9MF-^QZQlZ_Q# ' ZQ= Q~#\~Q#\ ?0Q~#'~Q'#>?DR≤#≤'B -&S2 ^_ ^ ^_ _ > B= − + C E&6:,+E&^Z^_?0_Ip9/0 $D.$6$ ,?9f.,>&S$-+&X.$IO+N7.,N7.,?0&S #Y6,S&?9f.,B.i.2 ^_ >^ B >_ ^B >_ B ' ' ' + + + = − + ÷ ' ' > lBC= ># B>#\B ># lB>' #B ' ' ' + + + − = − + ÷ = ' = ' 3 # # #\ # '# l# ` ' ' ' + + − + − + = − + ÷ ' ' ' ( =# =# = A = A ') ># B Q >T7># B # • V'€B ' ' l ' ' l ` ' + − = = − − ≤ × − ≥ ∀ ∈ − noM ^_ ') ` ≤ CU91g.,;PMF-⇔#Q ' Zc$+IS_> ' V l B Bài 4: (3,5 điểm) C -B $u76d.$&$U6IK*.,cd.$I+•9-6F9.,I+8# &H-#Y6TbM&9.,c$f.,I+•9-6b#Z6-&SQC :,+E&^&S$-+IK*.,&$‚7^?0^ ?9f.,,S&?@+.$-9?0I+•9-6F9.,I+8#&H-#ƒ+ IK*.,.i./0$D.$6$7+ 1B-+,S& · >,S&r6b#B?0 · >,S&.Y+ 6+v4B&„.,&$…. ¼ ^ .i.2 · · ' = C $K., · · ^= >$-+,S&IO+&H-$D.$6$7+ ^BC 7IS · · ^ ' = C 'C $u7,+P6$+v6⊥⇒/0#Y6IK*.,&-7&H-∆ >B X+&Sqq^>T7^/0$D.$6$7+BZ^⊥>?D · ^ A= >,S&.Y+6+v4&$…. .†-IK*.,6Fa.BB.i.⊥⇒/0IK*.,&-76$:$-+&H-∆ >'B |>B?0>'BN9MF-,+-7I+8#&H-?0&$d.$/06Fh&6b#&H-∆C =C nD/0IK*.,6F9.,6Fh&&H->,6B.i.∆&b.6X+C ∆^&S^Q>1E.cd.$&H->BB?0^Q>&X.$&H-$D.$6$7+^B.i. ^QQ^C7IS∆^/06-#,+E&Ip9 ⇒ · ^ (= ⇒ · '= ⇒ · · ( ' = = ∆&b.&S · (= .i./06-#,+E&Ip9C9MF-Q?0 · (= ]‚6 ∆_&S · ¼ _ NI_ ' = Z · ¼ _ NI_ ' = C‡6$UM ¼ ¼ NI_ NI_> .i. · · _ _> ⇒_ˆ_C Fi.I7X./UMI+8#N-7&$7_Q_C -#,+E&^_&b.6X+_&S · · _ (= = >,S&.Y+6+v4&„.,&$…. ¼ ^ B.i./0 6-#,+E&Ip9C9MF-_Q?0 · _ ( C= ]‚6∆_?0∆&S2 QZ_Q>B?0 · · · _> _ ( B= = − .i.∆_Q∆>&C,C&BC9MF-_QC |IS_\_\_Q\_\_Q'_C F7.,IK*.,6Fa.ZIK*.,cd.$/0TbM&9.,/@..$U6.i._≤' ⇒_\_\_≤lC 7IS6k.,>_\_\_BIX6,+E6FG/@..$U61g.,l ⇔_/0IK*.,cd.$&H->BC _0⊥>B.i._⊥⇒_/0IK*.,6F9.,6Fh&&H-⇒_Q_ ⇒ ¼ ¼ _ _= $-M_/0I+8#&$d.$,+‰-&H-&9.,.$jC noMI86k.,>_\_\_BIX6,+E6FG/@..$U61g.,l6$D_4$P+/0I+8#&$d.$ ,+‰-&H-&9.,.$jC Bài 5: (0,5 điểm) 2≤;≤=C$+IS1U64$KL.,6FD.$IW&$76KL.,IKL.,?@+2 = ; R =R ; ; l; '; + ≥ − + R ]‚6?v6FE+2 w6 ' 6 ; R =R ; 6 ' ' >; R B>=R ;B= + ≥ ⇒ = + 4TŠ.,1U6I[.,6$:&fRN+&$7$-+NOc$f.,b#Z6-&S2 ' >; R B>=R ;B ; = ; '≤ − + − = ⇒6 ' ≤'\'Ql⇒6≤'>T76≥BCU91g.,;PMF-⇔;Q'C R ]‚6?v4$P+2 -&S2 = ' ; l; '; >; ; ' 'B ' '− + = − + ≥ >T7 ' >; ; ' 'B− ≥B U91g.,;PMF-⇔;Q' $K?oM2 = ' ; R =R ; ; l; '; '≥ + ≥ − + ≥ +p9.0M&$t;PMF-c$+?0&$tc$+ = ; R =R ; ' ; l; '; ' + = − + = ⇔;Q'C noM1U64$KL.,6FD.$IW&$7&S.,$+J#T9M.$U6;Q'C . ! "#$%&'(') Môn thi: TOÁN $*+,+ /0#10+234$56 (không kể thời gian giao đề) Bài 1: (2,0 điểm) $71+896$:&2 ; ' ; ; '