ĐỀ THI THỬ ĐẠI HỌC LẦN III KHỐI A NĂM 2009 Môn Toán

Câu I (2 điểm). 1. Khảo sát và vẽ đồ thị hàm số y = x4 – 4x2 + 3 2. Tìm m để phương trình có đúng 4 nghiệm. Câu II (2 điểm). 1. Giải bất phương trình: 2. Giải phương trình: Câu III (2 điểm) 1. Tính giới hạn sau: 2. Cho hình chóp S.ABCD có đáy là hình thoi , . Hai mặt bên (SAB) và (SAD) cùng vuông góc với mặt đáy, hai mặt bên còn lại hợp với đáy một góc . Cạnh SA = a. Tính diện tích xung quanh và thể tích khối chóp S.ABCD.

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C N O N O N Oa b c abc a b c b c a c a b+ + + ≥ + + + + +  b%Mỗi thí sinh chỉ chọn câu Va hoặc Vb Câu Va (3 đimO5Chương trình cơ bản -5 H+W1/c1d9\2?=I9F'1c % ! C "x y∆ + − = 7*(9(E+N-e"OVTNCe@O5 f=1D+1HX9F'1c ∆ +\19(E+I CMA MB+ uuur uuur gL15 !5 H_$(7Q(K1d9\2?=hI(9F'1c% - - % ! ! x t d y t z t = −   =   = − +  7* ! % - C - x t d y t z t =   = +   = −  5i/ /FG1HD9F'1c9(^SN-e"e-O7*Ij1I6(9F'1c] - 7*] ! 5 C5 D+</`Ih1g+f% ! ! "z z+ = Câu Vb. (3 đim).Chương trình nâng cao -5 H+W1/c1d9\I(9F'1HZN - O%? ! B= ! >-C7*N ! O%N?kO ! B= ! >!MIj1S1R( N!eCO5l(m1/FG1HD9F'1c9(^S7*Ij1N - OVN ! O1n(]o=ISIJ9\]*( ,aS5 !5 H_$(7Q(K1d9\2?=hI(9F'1c% - - % ! ! x t d y t z t = −   =   = − +  7* ! % - C - x t d y t z t =   = +   = −  5i/ /FG1HD+W1IpSIJ9F'_P)*9R7S$JIISIq] - 7*] ! 5 C5HI&I</`Ih1g+f9(rS_(K - ! -z i+ + = V1D+</`IhIJ+]SgL15 sm1s N&,\I(1(_$(6(1PID1X+O ttu oS v \(]S (E+  ! - - wU> ¡ (Q(R% )(+ x y →±∞ = +∞ 4x,(m1(X%=y>@? C .? =y>" "V !x x⇔ = = ± T6,(m1(X ? −∞  !− " ! +∞ =y "B""B = +∞ +∞ C - - *+<9:,(m1HXI&I_6 ( ) ( ) !e" V !e− +∞ 7*;I,(m1HXI&I_6 ( ) ( ) e ! V "e !−∞ − *+<9R1IxI9R(1R(?>"V= U >C5*+<9R1IxI1(ES1R(?> !± V=  >- :1; = C  C− -  C -2 ? "!M "!M "!M "!M ! - :1;*+< @ ! @ Cy x x= − + = C =>) ! + - ? 2  C−  !− -- ! C 4<(K+Iq/FG1HD @ ! ! @ C )x x m− + = ,a<(9(E+Iq9:1;*+< "!M "!M @ ! @ Cy x x= − + 7*9F'1c=>) ! +5 li=/FG1HDIJ@(K+_(7*Iz_() ! +>"WI ! - ) + C< <  =+>-WI!{+{# "!M "!M  ! - - l(m1)R(,L1/FG1HD]FQ(]R M - M - ! ! " ! ! x x     − + + − ≤  ÷  ÷  ÷  ÷     W11> M - V "5 ! x t   + >  ÷  ÷   _(9J M - - ! x t   − =  ÷  ÷   TL1/FG1HDIJ]R 1B - ! ! " t − ≤  ! ! ! - "t t⇔ − + ≤  ! - ! -t⇔ − ≤ ≤ +  M - M - ! ! M - ! - ! - ! ) N ! -O ) N ! -O x x + +   + ⇔ − ≤ ≤ +  ÷  ÷   ⇔ − ≤ ≤ + "!M "!M "!M "!M ! - (rS_(K% -x ≥ FG1HD1FG9FG7Q( ! N - -O ! - !N -O "x x x x x− − − − − − − = N|O W1 -V "y x y= − ≥ 5(9JN|OIJ]R%? ! A?N=-OA!=A!= ! >"  N ! ON -O " ! "N - "O x y x y x y do x y ⇔ − + + = ⇔ − = + + ≠   ! ! - @ @ " ! x x x x x ⇒ = − ⇔ − + = ⇔ =  "!M "!M "M  ! - -  - ! - ! C ! C C - - - ! C ! C ! C C ! - - C ! C ! C C - - 1N -O - - 1N -O )(+ )(+ 5N -O - - - 1N -O )(+ 5N -O )(+ 5N -ON -O - - )(+N -O )(+N -ON -O # x x x x x x x x x e x e x x x x x e x x x x x x x x x x x x x − − → → − → → → → + − − − + − = + + − − − − = + + + + + + − − = + + + + + + = "!M "M "!M ! - }9F'I4Iq1+(&I4T5(9J ⊥ T N;)PC9F'7S$JIO]9J SIA β ∠ = 4 >5I1 β VT>U> I1 ( a β α V4> ( a β ! ! I1 5 5( ( ABCD a S AB AD β α α = =  C ! 5 I1 C( S ABCD a V β α =  4 ?^ >4 4T B4 4U 4 4T B4 4U T   > ! I1 - 5N- O ( ( a β α β + "!M "!M "!M "!M l - IJ C C C ! ! ! ! ! ! C N O N O N Oa b c abc a b c b c a c a b+ + + ≥ + + + + +  ! ! ! ! ! ! ! ! ! C ! ! ! ! C I I I ! a b c b c a c a b ab bc ca A B C + − + − + − ⇔ + + ≤ ⇔ + + ≤ W1_&I  ! ! ! ! I I I NI I O5- NI I ( ( O - - C ~NI I O - •B ~( B( T•I I ! ! ! A B C A B A B A B A B A sB + + = + − − ≤ + + = U9J C I I I ! A B C+ + ≤ "!M "!M "M l C - - d()*1HS9(E+IqTV€)*1HS9(E+IqT5(9JN-e!OV€N M e C ! − O IJ% C N O ! ! ! @MA MB MA MB MB MI MB MJ+ = + + = + = uuur uuur uuur uuur uuur uuur uuur uuur lD7i= CMA MB+ uuur uuur gL1_()*DI(mS7S$JIIq€1HX9F'1c ∆ F'1c€^S€7*7S$JI7Q( ∆ IJ/FG1HD%!?A=A.>"5 d9\9(E+)*(K+IqK ! ! C " M ! . " -# M x x y x y y −  =  + − =   ⇔   − − =   =   7i=N -# ! e M M − O "!M "!M "!M "!M ! - F'1c] - 9(^SN-e"e!O7*IJ7nI1Iz/FG)* - N -e!e-Ou = − ur V9F'1c ] ! 9(^STN"e-e-O7*IJ7nI1Iz/FG)* ! N-eCe -Ou = − uur 5 d( N OVN O α β )*I&I+W1/c9(^S7*)p)F[1I`] - 7*] ! 5F'1cIp1D+ IP)*(1S=mIq(+W1/c N O * N Ov α β IJ N"e"e COV N -e-e"OMA MB= − = − uuur uuur - - ! ! - e N!e-e"OV e N-e-e@O C n MA u n MB u     = = = − =     ur uuur ur uur uuur uur )*I&I7nI1/&/1S=mIq N O * N Ov α β F'(1S=mIq N O * N Ov α β IJ7nI1GIz/FG - ! e N@e .e-Ou n n   = = −   r ur uur 7*9(^S N-e"e-OXIJ/FG1HD?>-B@1V=>.1Vh>-B1 "!M "!M "!M "!M C - d(h>?B=5(5(9Jh ! >? ! A= ! B!?=5(V z x yi= − ! ! ! ! ! ! " ! !N -O " ! " N -e COVN "e "OVN !e "O !N -O " z z x y x x yi x y x x y x y x y x y + = ⇔ − + + − =  − + = ⇔ ⇔ = = ± = = = − =  − =  li=IJ@</`I1g+fh>"Vh>!7*h>- Ci± "!M "!M "!M "!M l, C - - d((9(E+1`(Iq9F'1cIp1D+7Q(N - O7*N ! O)p)F[1)*7* d(N?e=O ! ! - N O -CC x y∈ ⇒ + =  N-O lD)*1HS9(E+IqXN@A?ekA=O5 U ! ! ! N O N! O Nk O !MC x y∈ ⇒ + + − =  N!O •N-O7*N!O1IJK ! ! ! ! -C N! O Nk O !M x y x y  + =   + + − =   (6(K19F[IN?>!e=>CON)R(O7*N?> -‚ M − e=> k M O5li=N -‚ M − e k M O F'1cIp1D+9(^S7*IJ/FG1HD%?AC=B‚>" "!M "!M "!M "!M ! - d(N-1e!1e!B1O - d∈ VN1ye-BC1y-1yO ! d∈ F'1c] - IJ7nI1Iz/FG)* - N -e!e-Ou = − ur V9F'1c] ! IJ7nI1Iz /FG)* ! N-eCe -Ou = − uur 5 N ƒ -eC ƒ ! -e ƒ COMN t t t t t t= + − − + − − + uuuur )*9R7S$JIISIq] - 7*] ! _(7*Iz_( - ! 5 " ! ƒ C C " ƒ @ - " 5 " MN u t t t t MN u  = − + =   ⇔   − − = =    uuuur ur uuuur uur  C ƒ M ‚ M t t  =   ⇔   =   "!M "!M U9JN ! -@ C e e M M M − − OVN C -@ ! e e M M M O5 W1IpS9F'_PIJ,&_P> ! ! ! MN = 7*1o+N - -@ - e e -" M -" − OIJ /FG1HD ! ! ! - -@ - - N O N O N O -" M -" ! x y z− + − + + = "!M "!M C - d(h>?B=(VN?e=O)*9(E+,(ES](„</`Ih5 ! ! - ! - N -O N !O -z i x y+ + = ⇔ + + + = F'1HZNO% ! ! N -O N !O -x y+ + + = IJ1o+N-e!O 2 F'1c2IJ/FG1HD=>!? 4</`Ih1g+f9(rS_(K7*IJ+$]SgL1_(7*Iz_(9(E+ T(ES](„J1S\INO7*p<I1d9\2L1V9JIP)*+\11H( (9(E+Iq9F'1c27*NO  (9J1d9\IqJ1g +fK ! ! - - - - ! M M V ! ! N -O N !O - ! ! M M x x y x x y y y   = − − = − +   =    ⇔    + + + =    = − − = − +     h> - ! - N ! O M M i− + + − + "!M "!M "!M "!M   . abc a b c b c a c a b+ + + ≥ + + + + +  b%Mỗi th sinh chỉ chọn câu Va hoặc Vb Câu Va (3 đimO5Chương trình cơ bản -5 H+W1/c1d92?=I9F'1c %