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së gi¸o dôc vμ ®μo t¹o hμ tÜnh Trêng THPT NguyÔn Trung Thiªn §Ò THi thö ®¹i Häc LÇN I n¨m 2014 Môn thi: To¸n - KHỐI D Thời gian làm bài: 180 phút
sở giáo dục và đào tạo hà tĩnh Tr"ờng THPT Nguyễn Trung Thiên Đề THi thử đại Học LầN I năm 2014 Mụn thi: Toán - KHI D Thi gian lm bi: 180 phỳt I. Phần chung cho tất cả thí sinh (7,0 điểm) Câu I (2,0 điểm) !"# "$% &' 42 24 yxmx =+ () *+ ,"- () m C ./0 % 1$ ,"2% &' ,"3( 45 6"7# &8, &3 90:; ,"0<; .$ .= *+ ,"- (>2 "$% &' ?"0 % @ A A5BC% ,D, (7 (8( E08 ,F- (>2 % GH (8( *0H% (3( ,F- (>2 *+ ,"- () m C ;I% ,F<; (8( ,FJ( ,K2 *L5 Câu II (2,0 điểm) 45 M070 N"OP;E ,FC;"Q sin2cos2cos3sin2 xxxx +=+ 5 A5 M070 N"OP;E ,FC;" Q 222 41 2 log(4)2log8326 xx +=++ Câu III (1,0 điểm) M070 "R N"OP;E ,FC;"Q 222 710 1310 xyyx xyyxy ++= ++= Câu IV (1,0 điểm) !"# "C;" (")N S5TU!V () *8W TU!V 1$ "C;" ,"2;E .XY;E ,Z0 T .$ V5 U0:, TU @ A2 [ TV @ !V @ 2[ ST @ \2 .$ ST .XY;E E)( ./0 *8W5 B];" ,"H ,](" ?"'0 (")N S5U!V .$ ?"#7;E (8(" ,^ U *:; %N _S!V` ,"a# 25 Câu V (1,0 điểm) !"# \ &' ,"3( GOP;E bc Wc d5 !"e;E %0;" FI;E Q 222 0 xxyyyzzzx xyyzzx ++ +++ 5 II. Phần riêng (3,0 điểm): Thí sinh chỉ đ"ợc làm một trong hai phần (phần A hoặc phần B) A. Theo ch"ơng trình chuẩn Câu VI. a. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# ,2% E08( TU! () ,F3( ,i% j _4[k4`5 BFX;E *0H% (>2 (Z;" T! 1$ l_k4[ A`[ (Z;" U! () N"OP;E ,FC;" d:2xy +10 = 5 m8( *-;" ,K2 *L (8( *n;" (>2 ABC 5 Câu VII. a. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# *Oo;E ,Fp; 22 ():2220 Cxyxy += 5 qrN N"OP;E ,FC;" *Oo;E ,"g;E G (8(" E'( ,K2 *L %L, ?"#7;E 9I;E A .$ ,0:N bs( ./0 _!`5 Câu VIII. a. (1,0 điểm ) BC% "R &' (>2 2 x ,F#;E ?"20 ,F0H; ;"- ,"e( t0X,P; (>2Q () 2 2 n Pxx x =+ (0) x 5 U0:, FI;E ; ,"u2 %v;Q \ 32 1 352(1) nn CAn + = 5 B. Theo ch"ơng trình nâng cao Câu VI. b. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# "C;" 9C;" "$;" TU!V ,i% wc () G0R; ,](" 9I;E x5 y"OP;E ,FC;" *Oo;E ,"g;E :xy0 BC = 5 U0:, z_A[4` 1$ ,FX;E *0H% (>2 (Z;" TU5 BC% ,K2 *L *0H% w5 Câu VII. b. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# *Oo;E ,"g;E :4320 dxy += .$ *Oo;E ,Fp; 22 ():26150 Cxyxy ++= 5{0:, N"OP;E ,FC;" *Oo;E ,"g;E 1 d .XY;E E)( ./0 d (|, *Oo;E ,Fp; _!` ,Z0 T .$ U &2# ("# 6 AB = 5 Câu VIII. b. (1,0 điểm) !) 4A "K( &0;" E0u0 E+% \ "K( &0;" ?"'0 4A[ x "K( &0;" ?"'0 44 .$ } "K( &0;" ?"'0 4~5 !"K; ;EX ;"0<; 6 "K( &0;"5 B];" b8( &XD, &2# ("# %ỗ0 ?"'0 () ], ;"D, 4 "K( &0;"5 kkkkkkkkkkkkkkkkkkkkk Hết kkkkkkkkkkkkkkkkkkkk Đáp án K-D gồm có 5 trang. L"u ý : Mọi cách giải đúng đều cho điểm tối đa. Câu Đáp án và h"ớng dẫn chấm Điểm 1 (1,0 điểm) ________________________________________________________________________ {/0 %@A "$% &' ,Fở ,"$;" 42 44 yxx =+ +BrN b8( *-;"Q DR = + M0/0 "Z;Q lim x y = [ lim x y + = ________________________________________________________________________ _ S3 90:; ,"0<;Q 3 '48 yxx =+ c , 0 0 2 x y x = = = + U7;E 90:; ,"0<;Q b 2 ~ 2 + W + ~ k ~ + ~ k W ~ ~ kx kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk SXW F2Q j$% &' *+;E 90:; ,F<; %ỗ0 ?"#7;E ( ) ;2 .$ ( ) 0;2 5 j$% &' ;E"-(" 90:; ,F<; %ỗ0 ?"#7;E ( ) 2;0 .$ ( ) 2; + 5 Đ0H% (3( *Z0 (>2 *+ ,"- 1$ ( ) 2;0 .$ ( ) 2;0 5 Đ0H% (3( ,0HX (>2 *+ ,"- 1$ ( ) 0;4 5 ________________________________________________________________________ + Đ+ ,"- Q Đ+ ,"- (|, ,FJ( ,X;E ,Z0 ( ) 0;4 .$ (|, ,FJ( "#$;" ,Z0 *0H% ( ) 2;0 .$ ( ) 2;0 5 + t"r; bé,Q Đ+ ,"- _!` ;"r; ,FJ( ,X;E 1$% ,FJ( *'0 be;E5 ~cA} ~cA} ~cA} ~5A} Câu I. 2,0 điểm 2 (1,0 điểm) ________________________________________________________________________ B2 ()Q ( ) 32 '444 yxmxxxm =+=+ [ 2 0 '0 x y xm = = = ________________________________________________________________________ t:X 0 m ,"C ( ) m C ("n () %L, *0H% (3( ,F- .$ *) 1$ *0H% (3( *Z0 ;I% ,F<; ,FJ( ,X;E5 ________________________________________________________________________ t:X 0 m > ,"C ( ) m C () \ *0H% (3( ,F-5 zL, (3( ,0HX ;I% ,F<; ,FJ( ,X;E .$ "20 (3( *Z0 () ,K2 *L ( ) 2 ;4 mm c ( ) 2 ;4 mm 5 ________________________________________________________________________ ĐH "Z0 *0H% ;$W ;I% ,F<; ,FJ( "#$;" ,"C 2 402 mm == 5 {C 0 m > ;<; ("K; 2 m = 5 {rW ( ] { } ;02 m 1$ ;"ữ;E E08 ,F- (ầ; ,C% ,"u2 %v; W<X (ầX 9$0 ,#8;5 ~5A} ~cA} ~cA} ~5A} Câu II. 2,0 1 (1,0 điểm) ________________________________________________________________________ yB 2 2sincos12sincossin32 xxxxx +=+ ⇔ 2 (2sincoscos)(2sin3sin1)0 xxxxx −−−+= ⇔ (#&b_A&0;bk4` – _A&0;bk4`_&0;bk4` @ ~ ⇔ (2sin1)(cossin1)0 xxx −−+= ________________________________________________________________________ 1 sin 2 sincos1 x xx = ⇔ −= 1 sin 2 2 sin 42 x x π = ⇔ −= ________________________________________________________________________ 2 6 5 2 6 2 2 2 xk xk xk xk π π π π π π ππ =+ =+ ⇔ =+ =+ k ∈ ~c} ~c} ~cA} ®iÓm 2 (1,0 ®iÓm) ________________________________________________________________________ B2 () 22 12 2 2log8322log832 xx +=−+ ( ) 2 4 2log832 x=−+ ( ) ( ) 22 444 2log4log82log43 xx =−++=−+− 5 y"OP;E ,FC;" ( ) ( ) 222 44 log42log430 xx ⇔+++−= ________________________________________________________________________ §f, ( ) 2 4 log4 xt += c N"OP;E ,FC;" ,Fë ,"$;" 2 2301 ttt +−=⇔= [ 3 t =− 5 ________________________________________________________________________ {/0 , @ 4c ,2 () ( ) 2 4 log410 xx +=⇔= 5 {/0 , @k\c ,2 () ( ) 2 4 log43 x +=− _.Y ;E"0R%`5 {rW N"OP;E ,FC;" () ;E"0R% b @ ~5 ~c} ~cA} ~cA} C©u III. 1,0 ®iÓm t"r; bÐ, W@~ ?"Y;E ,"u2 %v; "R N"OP;E ,FC;" *v ("#5 jR N"OP;E ,FC;" *v ("# 2 2 1 7 1 13 x x yy x x yy ++= ⇔ ++= ________________________________________________________________________ §f, 1 ux y =+ [ x v y = 5 SXW F2Q 22 2 1 2 x ux yy =++ 22 2 1 2 xuv y ⇒+=− 5 6"0 *)c ,2 *Oî(Q 2 7 13 uv uv += −= 2 7 200 uv uu += ⇔ +−= 4 3 5 12 u v u v = = ⇔ =− = ________________________________________________________________________ ~cA} ~cA} ~cA} {/0 1 4 3 ux y x v y =+= == 3 1 34 xy y y = ⇔ += 2 3 3410 xy yy = ⇔ −+= 1 3 1 3 1 y x y x = = ⇔ = = ________________________________________________________________________ {/0 1 5 12 ux y x v y =+=− == 12 1 125 xy y y = ⇔ +=− 2 12 12510 xy yy = ⇔ ++= _.Y ;E"0R%`5 6:, 1Xr;Q jR N"OP;E ,FC;" *v ("# () "20 ;E"0R% 3 1 x y = = .$ 1 1 3 x y = = 5 ~cA} C©u IV. 1,0 ®iÓm V0R; ,](" "C;" ,"2;E TU!V 1$ () 2 13 2 22 a Saaa=+=5 V0R; ,](" ,2% E08( TUV 1$ 2 1 . 2 ABD SABADa ∆ == 5 V0R; ,](" ,2% E08( U!V 1$ 2 2 BCDABD a SSS ∆∆ =−=5 ________________________________________________________________________ B"H ,](" ?"'0 (")N S5U!V 1$ 23 . 11 3. 3322 SBCDBCD aa VSASa ∆ === 5 ________________________________________________________________________ B2 ()Q 22 910 SDaaa=+= 5 {C () SAABCD ⊥ SACD ⇒⊥ 5 zf, ?"8( ADCD ⊥ 5 SXW F2 CDSD ⊥ 5 V0R; ,](" ,2% E08( S!V 1$ 2 1 10 2 sCD Sa ∆ = 5 ________________________________________________________________________ MK0 G 1$ ?"#7;E (8(" ,^ U *:; _S!V`5 B2 ()Q 3 . 1 . 32 SBCDSCD a VdS ∆ == 3 2 3310 10 10 aa d a ⇔==5 ~cA} ~cA} ~cA} ~cA} C©u V. 1,0 ®iÓm B2 () ( ) 2 2 2 xxyxy xxyxy x xyxyxy +− − ==− +++ 5 V# bcW GOP;E ;<; 2 2 xyxy xy + ≤ + 5 SXW F2 2 22 xxyxyxy x xy −+− ≥−= + 5 ________________________________________________________________________ BOP;E ,3 ,2 (ò;E () 2 2 yyzyz yz −− ≥ + [ 2 2 zzxzx zx −− ≥ + 5 B^ *) &XW F2 222 0 222 xxyyyzzzxxyyzzx xyyzzx −−−−−− ++≥++= +++ _*N(%`5 ~c} ~c} A. Theo ch"¬ng tr×nh chuÈn C©u VI. a. 1,0 ®iÓm M07 &ö ( ) ;21 Cmm + 5 {C ( ) 1;2 E − 1$ ,FX;E *0H% T! ;<; ( ) 2;32 Amm −−−[ ( ) 3;42 AHmm =+−+ 5 ________________________________________________________________________ {C .a(,P ("n N"OP;E (>2 U! 1$ ( ) 1;2 BC u = 5 {C AHBC ⊥ ;<; ( ) .22420 BC AHumm =++−+= 1 m ⇔= 5 {rW (3;1) A − .$ (1;3) C 5 ______________________________________________________________ M07 &ö ( ) ;21 Bnn + 5 !) ( ) 1;22 BHnn =−−− [ ( ) 4;2 BC u = 5 {C BHAC ⊥ ;<; .4(1)2(22)0 BC AHunn =−+−−= 1 n ⇔= 5 {rW (0;1) B 5 ~cA} ~c} ~cA} C©u VII. a. 1,0 ®iÓm MK0 N"OP;E ,FC;" *Oo;E ,"g;E G 1$ 0 axbyc ++= ( ) 22 0 ab +≠ c 22 (;)22 c ddO ab =⇔= + 5 ________________________________________________________________________ §Oo;E ,Fp; () ,i% w_4[4` 98; ?];" R @A5 {C G ,0:N bs( ./0 _!` ;<; 22 (;)22 abc ddO ab ++ =⇔= + ________________________________________________________________________ SXW F2 abcc ++= 2 ba ab c =− ⇔ + =− ______________________________________________________________ {/0 ba =− c ("K; 1 a = 1;22 bc⇒=−=± ,2 *Oî( N"OP;E ,FC;" 220 xy −±= 5 {/0 2 ab c + =− c ,2 () 22 152150 aabb −+= 0 ab ⇔== _?"Y;E ,"u2 %v;`5 ~cA} ~cA} ~cA} ~cA} C©u VIII. a. 1,0 ®iÓm B^ *Ò 9$0c ,C% *Oî( ; @4\5 ________________________________________________________________________ 13 13 22(13) 13 0 2 2 kkkk k xCxx x −− = += ∑ 5 M070 ,C% *Oî( ? @85 ________________________________________________________________________ jR &' (Ç; ,C% 1$ 88 13 2. C 5 ~c} ~cA} ~cA} B. Theo ch"¬ng tr×nh n©ng cao C©u VI. b. 1,0 ®iÓm §Oo;E ,"I;E zw qX2 z .$ &#;E &#;E ./0 U! ;<; () N"OP;E ,FC;" b – W – 4 @ ~5 ________________________________________________________________________ 1 (,) 2 dMBC = [ 42(,).422 ABCD SdMBCBCBC=⇔=⇔= 2 2 BC MI ==5 ________________________________________________________________________ MK0 (;1) Iaa − [ 3 2 1 a MI a = =⇔ = ________________________________________________________________________ SXW F2 w_\[ A` "#f( w_4[ ~`5 ~cA} ~cA} ~5A} ~cA} C©u VII. b. 1,0 ®iÓm _!` () ,i% w_4[ k\`c 98; ?];" R @}5 {C 1 dd ⊥ ;<; N"OP;E ,FC;" *Oo;E ,"g;E 1 d () GZ;E 340 xyc ++= 5 ______________________________________________________________ 6"#7;E (8(" ,^ w *:; 1 d 1$ 1 9 (;) 5 c dId −+ = 5 zf, ?"8( 2 2 1 (;)2594 2 AB dIdR =−=−= 5 ________________________________________________________________________ SXW F2 9 4 5 c−+ = 920 c ⇔−+= 920 920 c c −+= ⇔ −+=− 29 11 c c = ⇔ =− ______________________________________________________________ {rW 1 d () N"OP;E ,FC;" 34290 xy ++= "#f( 34110 xy +−= 5 ~cA} ~cA} ~cA} ~cA} C©u VIII. b. 1,0 ®iÓm S' (8(" ("K; 6 "K( &0;" ,F#;E 4A "K( &0;" 1$ 6 12 924 C = 5 S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 4A .$ 44 1$ 6 7 C 5 S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 44 .$ 4~ 1$ 6 9 C 5 S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 4A .$ 4~ 1$ 6 8 C 5 ________________________________________________________________________ ⇒ S' (8(" ("K; 6 "K( &0;" &2# ("# %ç0 ?"'0 () ], ;"D, 4 "K( &0;" 1$ ( ) 6666 12798 805 CCCC−++=5 ________________________________________________________________________ {rW b8( &XD, (Ç; ,C% 1$ 805115 924132 P ==5 ~c} ~cA} ~cA} . sở giáo d c và đào tạo hà tĩnh Tr"ờng THPT Nguyễn Trung Thi n Đề THi thử đại Học LầN I năm 2014 Mụn thi: Toán - KHI D Thi gian lm bi: 180. 3. 3322 SBCDBCD aa VSASa ∆ === 5 ________________________________________________________________________ B2 ()Q 22 910 SDaaa=+= 5 {C () SAABCD ⊥ SACD ⇒⊥ 5