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 A, A1, B Thi gian lm bi: 180 phỳt I. Phần chung cho tất cả thí sinh(7,0 điểm) Câu I (2,0 điểm) !"# "$% &' 3 1 x y x = + () *+ ,"- .!/ 01 2"3# &4, &5 6789 ,"7:9 ;$ ;< *+ ,"- .!/ (=> "$% &'1 ?1 @78, A"BC9D ,EF9" ,78A ,GH89 (=> .!/ 678, I"#39D (4(" ,J D7># *7K% L (=> ? ,7M% (N9 (=> .!/ *89 ,78A ,GH89 6O9D 22 1 Câu II (2,0 điểm) 01 P737 A"BC9D ,EF9" 12sin(2)coscos3 4 x xx ++=+ 1 ?1 QR9"S L T 2 tanx 1os dx cx+ Câu III (1,0 điểm) P737 "M A"BC9D ,EF9"S 22 2 41 2 1 xyxyy y xy x ++= +=+ + Câu IV (1,0 điểm) !"# "F9" (")A U1VW!X () *4H VW!X Y$ "F9" ,">9D1 Z4H Y[9 VW T ?> \ W! T !X T XV T >\ UV ;G]9D D)( ;[7 *4H^ %_, A"`9D.UW!/ ,a# ;[7 *4H %b, D)( 60 o 1 QR9" ,"K ,R(" I"'7 (")A U1VW!X ,"c# >1 Câu V (1,0 điểm) !"# d &' ,"5( eBC9D f^ H^ g1 QF% D74 ,E- 9"h 9"i, (=> 67KG ,"j( S 222 222 ()()() 333 xyz Pxyz yzxzxy =+++++1 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) QE#9D %_, A"`9D ;[7 "M ,k> *b lfH ("# ,>% D74( VW! () ,Ek9D ,m% P .?\n0/1 ZBo9D ,EG9D ,E5( (=> (a9" W! () A"BC9D ,EF9" d:3xy40=1 ZBo9D ,"`9D VW () A"BC9D ,EF9" 1 :10310dxy++= 1 QF% ,k> *b (4( *p9" V^ W^ !1 Câu VII. a. (1,0 điểm) QE#9D %_, A"`9D ;[7 "M ,k> *b lfH ("# ">7 *7K% V.?\q/^ W.r\s/1 @78, A"BC9D ,EF9" *Bo9D ,Et9 .!/ ,78A fu( ;[7 ,Ev( "#$9" ,a7 *7K% V ;$ I"#39D (4(" ,J ,m% .!/ *89 W 6O9D w1 Câu VIII. a. (1,0 điểm ) QF% &' "a9D I"]9D ("j> f ,E#9D I">7 ,E7K9 () 3 2 n Pxx x =+ (0)x > 1 W78, EO9D 9 ,"h> %x9S 67898 2 332 nnnnn CCCCC + +++= 1 B. Theo ch"ơng trình nâng cao Câu VI. b. (1,0 điểm) QE#9D %_, A"`9D ;[7 "M ,k> *b lfH ("# ,>% D74( VW! ;G]9D (m9 ,a7 V.0\?/1 @78, A"BC9D ,EF9" *Bo9D ,Et9 .Q/ 9D#a7 ,78A ,>% D74( VW! 678, *Bo9D ,"`9D d:xy10= ,78A fu( ;[7 .Q/ ,a7 W1 Câu VII. b. (1,0 điểm) QE#9D %_, A"`9D ;[7 "M ,k> *b lfH ("# ">7 *Bo9D ,"`9D 1 :350dxy++=\ 2 :310dxy++= ;$ *7K% L.0\n?/1 @78, A"BC9D ,EF9" *Bo9D ,"`9D *7 yG> L (z, 12 ,dd Y{9 YB|, ,a7 V ;$ W &># ("# 22AB = 1 Câu VIII. b. (1,0 điểm) P737 A"BC9D ,EF9"S 3 2 2 2 loglog2 2 x x x += 1 nnnnnnnnnnnnnnnnnnnnn Hết nnnnnnnnnnnnnnnnnnnn §¸p ¸n K.A gåm cã 6 trang. L"u ý : Mäi c¸ch gi¶i ®óng ®Òu cho ®iÓm tèi ®a. C©u §¸p ¸n vµ h"íng dÉn chÊm §iÓm 1 (1,0 ®iÓm) ________________________________________________________________________ } QNA f4( *-9"S { } \1DR=− } U5 6789 ,"7:9S 2 4 '0 (1) y x => + ^ 1x∀≠− ^ &GH E> "$% &' *+9D 6789 ,E:9 (4( I"#39D ( ) ;1−∞− ;$ ( ) 1;−+∞ 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ } P7[7 "a9S lim1 x y →−∞ = \ lim1 x y →+∞ = T• Q7M% (N9 9D>9DS HT0 1 lim x y − →− =+∞\ lim x y →+∞ =−∞ T• Q7M% (N9 *j9DS fTn01 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ } W39D 6789 ,"7:9S f ∞− n0 ∞+ H’ } H +∞ 0 0 −∞ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ } Z+ ,"- S P7># ;[7 lfS .d\q/^ D7># ;[7 lHS .q\nd/1 Z+ ,"- 9"N9 L.n0\0/ Y$% ,m% *'7 fj9D1 x 0 -13 1 -3 q^?w q^?w q^?w q1?w C©u I. 2,0 ®iÓm 2 (1,0 ®iÓm) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ P73 &ö ( ) 00 ;Mxy ,"Gb( (C), 0 0 0 3 1 x y x − = + , 0 1x ≠− . 2"7 *) A"BC9D ,EF9" ,78A ,GH89 ∆ ,a7 M Y$S () () 0 0 2 0 0 3 4 1 1 x yxx x x − =−+ + + () ( ) 2 2 000 41630xxyxx⇔−++−−= ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Q"c# *Ò S ( ) ,22dI∆= () ( ) () 0 2 2 00 4 0 4163 22 161 xxx x −−++−− ⇔= ++ ()() 42 00 181160xx⇔+−++= q1?w q1?w 0 0 1 3 x x =  ⇔  =−  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @[7 0 1x = ^ A"BC9D ,EF9" :2yx∆=−\ @[7 0 3x =− ^ A"BC9D ,EF9" :6yx∆=+1 q^w 1 (1,0 ®iÓm) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ PQ 1sin2cos22coscos2 x xxx⇔++= 2 2cos2sincos2coscos20xxxxx⇔+−= ( ) ( ) 22 2coscossincossin0xxxxx⇔+−−= ( ) ( ) coscossin1cossin0xxxxx⇔+−+= ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cos0 cossin0 cossin1 x xx xx =   ⇔+=   −=  2 tan1 1 cos 4 2 xk x x π π π  =+   ⇔=−     +=     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2 4 2 xk xk xk π π π π π  =+    ⇔=−+   =    k ∈  q^?w q^w q^?w C©u II. 2,0 ®iÓm 2 (1,0 ®iÓm) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Q> ()S 22 tansincos 1coscos(1cos) xxx Idxdx xxx == ++ ∫∫ Z_, 2 costx= 2sincosdtxxdx⇒=− UGH E>S 1 2(1) dt I tt =− + ∫ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 11111 ln 212 t IdtC ttt +  =−=+  +  ∫ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 28, YGN9S 2 2 11cos ln 2cos x IC x  + =+   1 q^?w q^w q^?w C©u III. 1,0 ®iÓm N"N9 fÐ, HTq I"]9D ,"h> %x9 "M A"BC9D ,EF9"1 q^?w www.VNMATH.com HM ,BC9D *BC9D ;[7 2 2 1 4 2 1 x xy y y xy x  + ++=     +=+  +  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Z_, 2 1x u y + = ^ ; T f } H1 HM ,Eë ,"$9"S 4 1 2 uv v u +=    =+   P737 "M ,> ()S G T0 ; T d ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @[7 2 1 1 2 11 3 2 3 5 x x y u y v x xy y =    +  = ==    ⇒⇔   = =−    +=  =    q^?w q^?w q^?w C©u IV. 1,0 ®iÓm Pk7 N Y$ ,EG9D *7K% VW1 A B C D N 60 0 Q> ()S AN // DC AN = DC = a    9:9 VX!N Y$ "F9" 6F9" "$9"1 UGH E>S N! T VX T > T• NV T NW T N! T> ">H ACB∆ ;G]9D ,a7 ! &GH E> ACBC⊥ 1 X# ()SAABCD⊥ 9:9 SABC⊥ 1 ¸A ev9D *-9" Yý 6> *Bo9D ;G]9D D)( ,> &GH E> SCBC⊥ 1 UGH E>S P)( D7÷> .UW!/ ;$ .VW!X/ Y$ SCA∠ T• 60SCA∠=° ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ M_, I"4(S NBC∆ *ÒG 9:9 60NBC∠=° 3 3 2 ACABa== .tan603.33SAACaa=°== ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2 33 4 ABCD a S = ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ QR9" *B|( ,"K ,R(" (")A U1VW!X 6O9D 3 33 4 a 1 q^?w q^?w q^?w q^?w C©u V. 1,0 ®iÓm Q> () S 333222 2 3 x yzxyz P xyz  ++++ =+   ¸A ev9D 6i, *`9D ,"j( 22 2,,ababab+≥∀ 222 x yzxyyzzx⇒++≥++1 (§¼ng thøc x¶y ra khi x=y=z) 333 2 3 x yzxyyzzx P xyz  ++++ ⇒≥+   333 222 333 xyz P x yz  ⇒≥+++++   ________________________________________________________________________ XÐ, "$% &' 3 2 () 3 t ft t =+ ;[7 , • q \ 2 2 2 '()ftt t =− \ 4 '()02ftt=⇔= 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ W39D 6789 ,"7:9S , q 4 2 ∞+ H’ n q } H +∞ +∞ 4 8 32 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @NH 4 48P ≥ 1 Z`9D ,"j( f3H E> I"7 4 2xyz=== ">H 4 48P = 1 q^?w q^?w q^?w q^?w A. Theo ch"¬ng tr×nh chuÈn C©u VI. a. 1,0 ®iÓm Pk7 M Y$ ,EG9D *7K% W!^ ;F Md∈ 9:9 M .%\ d%ns/1 M$ 2GAGM=−  9:9 V .rn?%\ wnr%/1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ AAB∈ 2m⇒= ( ) 2;2M⇒ ^ ( ) 2;7A − 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ W! yG> M ;$ ;G]9D D)( ;[7 e 9:9 () A"BC9D ,EF9" f } dH – 8 T q1 BABBC=∩ 9:9 ( ) 1;3B − 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ M Y$ ,EG9D *7K% W! 9:9 ( ) 5;1C 1 q^?w q^?w q^?w q^?w C©u VII. a. 1,0 ®iÓm Pk7 00 (;)Ixy Y$ ,m% (=> *Bo9D ,Et9 .!/1 2"7 *)^ e# .!/ ,78A fu( ;[7 lf ,a7 V 9:9 ;[7 (0;1)i =  Y$ ;c(,C *C9 ;- ,E:9 ,Ev( lf^ ,> ()S IAi⊥  ( ) ( ) 00 1.10.00xy⇔−+−= 0 2x⇔=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Q"c# D73 ,"78,^ ,> ()S R T LW – w 2 ;25IB = ()() 22 0 26425y⇔−+−= 0 43y⇔−=± 0 0 7 1 y y =  ⇔  =  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ q^?w q^?w @[7 0 7y = ,"F (2;7)7IR⇒=1 @[7 0 1y = ,"F (2;1)1IR⇒=1 @NH ,> () ">7 *Bo9D ,Et9 ({9 ,F%S ()() 22 2749xy−+−=\ ()() 22 211xy−+−= q^w C©u VIII. a. 1,0 ®iÓm ¸A ev9D (]9D ,"j( 11 1 kkk nnn CCC ++ + +=^ ,> ()S 6789 33 nnnn CCCC+++ 677889 2() nnnnnn CCCCCC=+++++ 789 111 2 nnn CCC +++ =++ 89 22nn CC ++ =+ 9 3n C + = P73 ,"78, ,BC9D *BC9D ;[7 98 32 2 nn CC ++ = 3 2 9 n + ⇔= 15n⇔= 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2"7 *) () 3 2 n Pxx x  =+   () 15 15 3 15 0 2 k k k K Cx x − =  =   ∑ 305 15 6 15 0 2 k kk K Cx − = = ∑ 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ U' "a9D I"]9D ("j> f ,BC9D j9D ;[7 305 06 6 k k − =⇔=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ U' "a9D A"37 ,F% Y$ 66 15 .2320320C = 1 q^?w q^?w q^?w q^?w B. Theo ch"¬ng tr×nh n©ng cao C©u VI. b. 1,0 ®iÓm Pk7 L Y$ ,m% (=> *Bo9D ,Et9 9D#a7 ,78A ABC∆ 1 @F ABC∆ ;G]9D (m9 ,a7 V 9:9 L Y$ ,EG9D *7K% W! ;$ AIBC⊥ 1 Q"c# D73 ,"78, ()BCd⊥ //dAI⇒ ⇒ W49 IR9" (=> .Q/ Y$S (,)2RdAd==1 ()BCd⊥ ⇒ W!S f } H } ( T q1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (,)2dAdR== 12 2 2 C++ ⇔= 1 5 C C =−  ⇔  =−  UGH E> :10 :50 BCxy BCxy +−=   +−=  ZBo9D (># VL (=> ABC∆ *7 yG> ( ) 1;2A ;$ &#9D &#9D ;[7 ():10dAIxy⇒−+= 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ N8G :10BCxy+−= 10 : 10 xy IBCAI xy +−=  ⇒=∩  −+=  ⇒ L.q\0/1 UGH E>S () 2 2 ():12Txy+−=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ N8G :50BCxy+−= 50 : 10 xy IBCAI xy +−=  ⇒=∩  −+=  ⇒ L.?\d/1 UGH E>S ()() 22 ():232Txy−+−=1 @NH () ">7 *Bo9D ,Et9S () 2 2 12xy+−= ;$ ()() 22 232xy−+−=1 q^?w q^?w q1?w q^?w C©u VII. b. 1,0 ®iÓm @F 1 Ad∈ ^ 2 Bd∈ 9:9 Dk7 ,k> *b (;35)Aaa−−\ (;31)Bbb−−1 ( ) ;43()ABbaba=−−−  1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ QJ D73 ,"78, 22AB = &GH E>S ()() 2 2 4322baba−+−−=  1 Z_, tba=− ^ ,> ()S () 2 2 2 348 2 5 t tt t =   +−+=⇔  =  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @[7 2t = 2ba⇒−= (2;2)AB⇒=−  Y$ ;c(,C ("p A"BC9D (=> ∆ ({9 ,F%1 UGH E> A"BC9D ,EF9" *Bo9D ,"`9D (=> ∆ Y$ 12 22 xy−+ = − 10xy⇔++=1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @[7 2 5 t = 2 5 ba⇒−= 1 QBC9D ,5 ,> () A"BC9D ,EF9" *Bo9D ,"`9D (=> ∆ Y$ 790xy−−=1 @NH () ">7 *Bo9D ,"`9D ({9 ,F% Y$ 10xy++= ;$ 790xy−−=1 q^?w q^?w q^?w q^?w C©u VIII. b. 1,0 ®iÓm ZIS 0x > ^ 1 2 x ≠ 1 PQ 3 2 2 2 log 2 2 2log2 log2 x x x     ⇔+=   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2 2 2 3log1 1 21log2 1log2 x x x −  ⇔+−=  +  2 2 2 3log1 log0 1log x x x − ⇔−= + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Z_, 2 logtx= ^ ,> ()S 31 0 1 t t t − −= + 31(1)0ttt⇔−−+= 2 210tt⇔−+= 1t⇔= ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @[7 1t = 2 log1 x ⇒= 2x⇒= 1 @NH A"BC9D ,EF9" () 9D"7M% f T ? 1 q^?w q^?w q^?w q^?w . giáo dục 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 A, A1, B Thi gian lm bi: 180 phỳt I. Phần chung cho tất cả thí sinh(7,0