TỔ TOÁN - TIN ĐỀ THI THỬ THPT QUỐC GIA NĂM 2015 – LẦN 2 MÔN: TOÁN Câu 1. ( ) + = + !"#$% #&%''()* +,- ".)/)01%2 3%2 4 = + + ,5 6##)#/78%"#9 :'; ,"#/< =, = + )6 2# >+%?%@ 'A#BC2, D)E Câu 2. ##70F%2 >.%4 ( ) , , #% G + − = "H%I)<%,-7=, ! = − + Câu 3."###70F%2 >.% C2 J C2 J − + − = Câu 4."##970F%2 >.% J J J J J K − − + − = − ∈ − + − = − ¡ Câu 5."H% H,78% L J $ = + ∫ Câu 6. " .%,M7 % & ,M)N & C.% #,6% M, · G OG = K.%,#$<,- % >&%P ( ) & >Q%2'A# >D%2 8,- 2#, ∆ RP 73%2 ( ) S: T7 'A# P 73%2 ( ) :;U 2M, G OG H% / H, V# ,M7 % & 'V%2,, W )$%P 73%2 ( ) %& X Câu 7.">%2P 73%2 D)EBYNK,.% %2:;U'<I%2 6#:'UK UZ'U[:;D#C.%,#$<'<I%22M,,-UC&%:\#/ Z L L ' ÷ C ><%2)#/,-,)+%,, D)E,,)#/:K;K,-.% %2"#$ ; <E, )01%2 3%2 4 G ∆ − + = Câu 8. ") >%2VI%22#%BYN], 4 Y N ] J G − + + = K)01%2 3%2 Y J N ] ^ 4 J − + − = = − K Y J N O ] ^ 4 O L − − = = − . R ^ K ^∈ ∈ ,R%2%2 'A#'V%2,, WR)$% ( ) "_%2 Câu 9. "# RE E7)!%2'#&%"#)0T,)% W)$%`@N%2a<%#&% '#&%"#>*#,E%2,, >&%'#&%"#C6#'A#%<H%Y,<@ )/V$ b< <)0T,CE Cc Câu 10 " K K ( C" !,^0F%2=%2#%>_%24 ( ( ( ( + + + + + ≥ + + + + + Câu/ ý HƯỚNG DẪN CHẤM Thang điểm d\4 ¡ e − dS;4 ( ) f GK − = < ∀ ≠− + L ZJZ JZ$ ( ⇒ ∈ ⇒ = ⇒ − GL %2+,"#$% >&%,,V%2 Z −∞ − ÷ ' Z − +∞ ÷ H%2#A#6%' #9,g% GL `g7"%2"#$% #&% GL d\* +4#BY4hZGZ#BN4GZi()j%2)* + GL " %)E2#)#/4 Z + = + + ≠ − + G ⇒ + + − = KZ\P ( ) = + + − GKL d^,5 6##)#/78%"#9 ⇔ ,M#%2#978%"#9 V,hk ⇔ G f G G G ≠ ∆ = > ⇔ > − ≠ ÷ GKL dD#%)E,,2#)#/:';C K . K C,,%2#9,- ⇒ + =− − = M4B: lB; [ ( ) ( ) + + + + + + + [ ( ) ( ) ( ) ( ) ( ) + + + + + + + [ ( ) ( ) ( ) − + − − + + + ÷ GKL [ L + + L m ≥ + = n7^o%2;\,I#'.^0F%2 GKL U@<"_%2YN> ⇔ = )*Z`4 = C2# >+,p% . ( ) , , #% G + − = , G #% π = ⇔ + = ÷ GKL liA# ( ) , G + + π π = ⇔ = + ∈ ¢ liA# #% + + + π π π π = + = ⇔ ∈ ÷ = + ¢ GKL " J J O q ! = − + = − + + = − + = + − − = − GKL igN L L! ! = − ⇒ = + = GKL J C2 J C2 J − + − = \\4YrJd iA#\d ⇔ [ ] C2 J J − − = ⇔ J J − − = GKL ⇔ L = − = )#,#$<)#s<V#9% ,M%2#9,-Y[L GKL \\4 G GK K − ≥ ≥ ⇔ ≥ ≥ ≥ ≥ g%Yt K ≥ = VI%2C%2#9,-9t > .7 ,-9u J G + − − − + − − = J G ⇔ + − + = ÷ − − − GKL K G = > − #)MK7 >v % ( ) ( ) J J G J G + + − = ⇔ − + + + = ⇔ = GKL iA# [K . = ⇔ = + − K $'7 K )0T, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) J J J J JJ J J JJ J J G O G O G − − + − = − ⇔ − − + − − − = − − ⇔ − − + = − + + − − + − − − ÷ ⇔ − − + = ÷ ÷ − + + − − + − GKL ( ) L G + ⇔ − − = ⇔ = ≥ iA# L J L + + = ⇒ = \#,#$<\K970F%2,M%2#9 ( ) L J L Z Z + + = ÷ ÷ GKL L \P J K G J − = + ≥ ⇒ = J ⇒ = \w#,g%4 Z L = → = = → = GKL $ = − ∫ $ ⇔ = − − + ∫ GKL ( ) C% C% $ = − − + GKL C%J C%L$ = − GKL O O S A D C B H E dD# & = ∩ ,M4 · G K OG % % ⊥ ⊥ ⇒ = t 2#,SB'<I%2 6#4 G G J % OG % OG J O %, %, , , = ⇒ = = = GKL ,M4 2#,:;)s<4 J & % % = = igN J J J J J % & & - %, %= = = )' GKL dH%V?%2,, >%2 % & Vc . %,P V#)M ,M4 Z Z & . )I#E '<I%22M,i4 J J Z Z q & .= = = GKL n7^o%2,I%2 =,4 K %& & . = + + J ⇒ = R ( ) ( ) O K K %& %&= = GKL x D#yC ><%2)#/U @N:;RyC.%".%%%&% '. &⊥ K%&%yC >!, 8 2#,:UR . '& ⇒ ⊥ . '⊥ %&% &' &'⊥ GL W)M<N>70F%2 >.% 4J O ' + = D)E;C%2#9,-9 { Z J O − = − ⇒ + = GL D#uC2#)#/,-:';UK ,M G G Z J J $ &$ $ $ & $ = = ⇒ = ⇒ uuur uur 0F%2 >.%)01%2 3%2 4 G + = 0F%2 >.%)01%2 3%2 4 &, − = <N> D)E q Z L L , <N> D)E OZ GL W Z$ $ = ⇒ uur uur GL : ; U u R 8 ,M Y J ^ 4 N J ] = + = − − = + K Y J O< ^ 4 N O < ] L< = + = + = − S<N> ( ) R J Z J Z + − − + ( ) J O<ZO <Z L<+ + − GL ,M ( ) R O< ZG < J Z L< − + + − − − uuuur KiX, F77 <N$%,- ( ) 7 % Z Z= − uur 7 R% G < G= ⇔ + + = uuuur uur GL ( ) ( ) q ^ RK ^ RK J + = = X2# #$ <N> q O + = ⇔ = − ∨ = − GL # < = − ⇒ = − 0F%2=%2 ,M ( ) R Z ZG− K ( ) JZZL− # < G = − ⇒ = 0F%2=%2 ,M ( ) R ZZ − − K ( ) JZOZG GL 9 D# Ω C g7T7,,,,C@N>'#&%"# W'#&%"#"%)p<K ,M ( ) % JJGΩ = = GL S,,'#&%"#)%CcCOK,,'#&%"#)%,z%CL D#:C"#$%,C@N>'#&%"#,M w%2CE Cc >%2'#&%C@N>,M'#&%"#CcKJ'#&%"#,z%S<N>,M J O L OG OG= = ,, >%2'#&%C@N>,MJ'#&%"#CcK'#&%"#,z%KS<N>,M J O L GL GG= = ,, GL igN ( ) J J O L O L % : OG= + = S<N> ( ) ( ) ( ) % : OG O : % JJG JJ = == = Ω GL 10 ,M ( - ( ( = + + + + + ÷ ÷ ÷ ( ( ( ( ≥ + + = + + ÷ GL RP V,4 Z Z ( ( ( ( + ≥ + ≥ + ≥ E%2 X'$,,;\ >&% )0T,4 ( ( ( + + ≥ + + GL S<N>4 - ( ( ( ≥ + + = + + + + + ÷ ÷ ÷ ÷ - ( ( ( ( ≥ + + = + + = + + + + + + \3%2 =,YN>V#',{V#4 ( = = = GL /0(1(+1(23435/(6(74(/1(489:(; . TỔ TOÁN - TIN ĐỀ THI THỬ THPT QUỐC GIA NĂM 20 15 – LẦN 2 MÔN: TOÁN Câu 1. ( ) . & >Q %2 'A# >D %2 8,- 2# , ∆ RP 73 %2 ( ) S: T7 'A# P 73 %2 ( ) :;U 2M, G OG H% / H, V# ,M7 % & 'V %2 ,,. > %2 VI %2 2# %BYN], 4 Y N ] J G − + + = K)01 %2 3 %2 Y J N ] ^ 4 J − + − = = − K Y J N O ] ^ 4 O L − − = = − . R ^ K ^∈ ∈ ,R %2 %2 'A#'V %2 ,,