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8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
1/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
TRNG TRUNG HC PH THNG TH X CAO LNH--------------
TP TH LP CHUYN TON NIN KHA 2006 2009
Nguyn c Tun -
TUYN TP CC THI TH
I HC , CAO NGTRN TP CH
QUA CQUA CQUA CQUA CCCCC NNNNMMMM
---- Thng 03-2009 ----
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
2/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2003
THI THI HC, CAO NG S 1Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s: .424 mxmxxy ++=
1. Kho st v v th hm s khi .0=m 2. Tm cc gi tr ca m th hm s c ba im cc tr sao cho tam gic c nh l ba im cctr nhn gc ta lm trng tm.
Cu II: (2 im)1. Gii cc phng trnh :
( ) ( )( )xx xxxx = 2002loglogloglog 20022002
2. Tm tt c cc gi tr ca a tp xc nh ca hm s ( )xa
xaxf
+=
2
2cha tp gi tr ca hm
s ( ) .242 12 ++=
axxxg
Cu III: (2 im)1. Gii phng trnh :
( )xxxx 141488 sincos64sincos +=+ 2. Hai ng cao 11 ,BBAA ca tam gic nhn ABC ct nhau ti H. Gi R l bn knh ng trnngoi tip tam gic ABC.Chng minh rng din tch tam gic 11BHA bng CBACR cos.cos.cos.2sin.
2 .
Cu IV: (2 im)1. Cho t din OABCc: 0180 AOB BOC+ = gi l OD ng phn gic trong ca gc AOB
Hy tnh gc
BOD .2. Trong khng gian vi h ta cc vung gc Oxyz cho hai ng thng :
( )2 1 0
1 0
x y
x y z
+ + =
+ = ( )
3 3 0'
2 1 0
x y z
x y
+ + =
+ =
a. Chng minh rng hai ng thng ( ) v ( )' ct nhau.
b. Vit phng trnh chnh tc ca cp ng thng phn gic ca cc gc to bi ( ) v ( )' .
Cu V: (2 im)
1. Tnh tch phn :( )
24
4 2
4
sin
cos tan 2 tan 5
xdxI
x x x
= +
2. Trong hp ng 2n vin bi c n vin bi ging ht nhau v n vin bi xanh i mt khc nhauHi c bao nhiu cch khc nhau ly n vin bi t hp .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2003:
Cu I:
1. Cc bn t gii.2. p dng n l Vi-t bc ba. p s: : 6.m =
Cu II:
1.p s: 1001.x =
2.p s:3 17
.8
a+
>
Cu III:
1. Phng trnh v nghim. p dng BT Cauchy.
2. Cc bn t gii.
Cu IV:
1.p s: 090 .BOD =
2.
a. Chng minh h c nghim duy nht.
b. Dng vectn v.
p s:
1 32 2 ;
1 1 2 2 3 5
14 30 14 30 14 301 32 2 .
1 1 2 2 3 5
14 30 14 30 14 30
x zy
x zy
+
= =
+ + +
+
= =
Cu V:
1.t tant x= . p s: 32 ln 2 .8
I =
2.p s:0
2 .n
k n
n
k
C=
=
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
4/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2003
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s : 423 += axxy 1. Kho st v v th hm s khi .3=a 2. Tm a phng trnh 423 ++ maxx = 0 lun c 3 nghim phn bit, vi mi gi tr ca mtha iu kin : .04
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2003:
Cu I:
1. Cc bn t gii.2. Lp bng bin thin.
p s: 3a .
Cu II:
1. p dng BT B.C.S. p s:1
2x y= =
2.p s:1
2.
Cu III:
1.t2 1 1
.3 10
xt t
x
+ =
p s:
1 2; .
3 4 5 4x
=
2. Cc bn t gii.
Cu IV:
1.p s:
25
.24V a h=
2. p s:6 6
.2 2 2 2
m
<
+ +
2. Tnh1
2 2
0
4 3I x x dx =
Cu IV: (2 im)1. Cho ng thng ( )d : 2 2 0x y = v hai im (0;1)A v (3;4)B . Hy tm to ca im
M trn ( )d sao cho 2 22MA MB + c gi tr nh nht.
2. Cho ng parabol c phng trnh 2 4y x= v gi s F l tiu im ca n. Chng minh rngnu mt ng thng i qua F v ct parabol ti hai im A, B th cc tip tuyn vi parabol ti A ,B vung gc vi nhau .
Cu V: (2 im)1. T cc ch s 0, 1, 2, 3, 4, 5, 6 ta c th vit bao nhiu ch s t nhin c 5 ch s khc nhau sao
cho trong nht thit c cc ch s 1 v 2 .2. Cho , ,x y z l cc s thc tho mn iu kin sau :04,01,01,0 >+>+>+=++ zyxzyx .
Hy tm gi tr ln nht ca biu thc:
1 1 4
x y zQ
x y z= + +
+ + +.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2005:
Cu I:
1. Cc bn c th t gii .
2. Hm s c cc i , cc tiu khi PT ' 0y = c hai nghim phn bit khc 1.
p s:4
13
m< < .
Cu II:
1.p s:f(0)=0.2. Ch s dng
3
3
4 sin 3 sin sin 3
4 cos 3 cos cos 3
x x x
x x x
=
= +
p s: ( )6
x k k Z
= + .
Cu III:
1. p s: 1 0x < <
2. C tht 3 2 sinx t=
p s: 2 1129 3
I = + .
Cu IV:
1. p s: (2;0)M 2. Cc bn t chng minh.
Cu V:
1. p s: 1056 s2. t 1, 1, 4a x b y c z = + = + = + , th , , 0, 6a b c a b c > + + = .
p s: max1
3Q = khi
1
2x y= = v 1z = .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2005
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
1. Kho st v v th ca hm s :
2 2
3
x xy x
= .
2. Tnh din tch ca hnh phng c gii hn bi th ca hm s v trc honh .
Cu II: (2 im)1. Gi s , , ,a b c dl cc s thc tha mn ng thc : 2( ) ( )ab b c d c a b+ + + = + .Chng minh rngtrong ba bt phng trnh :
2 2 20 : 0 : 0x ax b x bx c x cx d + + + t nht mt bt phng trnh c nghim .
2. Vi nhng gi tr no ca a th h phng trnh :
2 2 2 2
1 1
x y a
a
x y
+ = + + =
c ng hai nghim?
Cu III: (2 im)1. Gii phng trnh lng gic:
1cos .cos2 .cos3 sin .sin2 .sin 3
2x x x x x x = .
2. Cho 3 4 4( ) (1 ) f x x x x = + + + .Sau khi khai trin v rt gn ta c :2 16
0 1 2 16( ) ...f x a a x a x a x = + + + + .Hy tnh gi tr ca h s 10a .
Cu IV: (3 im)1. Trong mt phng vi h trc to-cc vung gc Oxy cho Elip (E) c phng trnh l
2 2
2 21
x y
a b+ = (vi 0, 0a b> > ).Gi s ,A B l hai im thay i trn (E) sao cho OA vung gc
vi OB.
a. Tnh 2 21 1
OA OB + theo a v b .
b. Gi H l chn ng vung gc h tOxung AB .Tm tp hp cc im H khi ,A B thay i trn(E).
2. Cho hnh lp phng . ' ' ' 'ABCD A B C D vi cnh bng a . Hy tnh khong cch gia cnh'AA vi ng cho 'BD theo a
Cu V: (1 im)Cho , ,x y z al nhng s dng tha mn 1xyz = . Tm gi tr nh nht ca biu thc:
9 9 9 9 9 9
6 3 3 6 6 3 3 6 6 3 3 6
x y y z z x P
x x y y y y z z z z x x
+ + += + +
+ + + + + +.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2005:
Cu I:
1. Cc bn c th t gii.
2. p s:15
8ln22
S = .
Cu II:1. Cc bn t chng minh.
2. p s: 2 2a < < .
Cu III:
1.p s: ; ; ( ).8 2 12 3 4
x k x k x k k Z = + = + = +
2. Cc bn c th bin i4 4
3 3( ) 1 (1 ) (1 )(1 ) f x x x x x x = + + + = + +
p s: 10 22a = .
Cu IV:1.
a. p s:2 2
2 2 2 2
1 1 a b
OA OB a b
++ =
b. p s: Tp hp H l ng trn tm (O;2 2
2 2
a b
a b+)
2. p s:2
2
a.
Cu V:
Ch rng vi , 0a b > ta lun c:2 2
2 2
1
3
a ab b
a ab b
+
+ +
p s: min 2P = khi 1x y z= = = .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2005
THI THI HC, CAO NG S 3Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s
3 2
( 3) (2 3 ) 2 .y x m x m x m = + + +
(1)1. Kho st v v th ca hm s vi
3
2m = .
2. Tm trn mt phng cc im cnh m thi hm s lun i qua vi mi m.3. Tm m th ca hm s ct trc honh ti ba im phn bit c honh lp thnh mt cps cng theo mt th t no .
Cu II: (2 im)1. Cho tam gic ABC c ba gc , ,A B C tho mn:
2 3tan tan
2 2 3
cos cos 1
A B
A B
+ =+ =
Chng minh rng tam gic ABC u.2. Gii bt phng trnh :
2
24
1 1
log (3 1)log ( 3 ) xx x .
2. V1
3x > nn 2 3 3 1.x x x+ > > T ta thy v tri ca phng trnh dng.
p s:2
13
x< < .
Cu III:
1.t x t= , sau khi th vo cc bn nhn thm lng lin hip.p s: 2lnI a= 2. p s: 6; 0a b= = .
Cu IV:
1. p s: (1;1;1)I ,( ) : 2 1 0Q x y =
2. p s:1 2
7 14 22
x y z+ = =
3. p s: 1; 1 3a b= < < .
Cu V:
2 2 2 2 2 2
2 2 2 2 2 2
5 cot 16 cot 27 cot (3 2) cot (12 4) cot (9 18) cot
(3 cot 12 cot ) (4 cot 9 cot ) (18 cot 2 cot ) 12
F A B C A B C
F A B B C C A
= + + = + + + + +
= + + + + +
p s: min 12F = khi1 1
cot 1, cot , cot2 3
A B C= = = .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2005
THI THI HC, CAO NG S 4Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
1. Kho st v v th ca hm s : 3 3 2y x x= + (C)2. Gi s , ,A B C l ba im thng hng phn bit thuc (C), tip tuyn vi (C) ti , ,A B C tng ngct li (C) ti ', ', 'A B C .Chng minh rng ', ', 'A B C thng hng .
Cu II: (2 im)1. Gii h phng trnh:
2
2
1 1
1 3
x y
y x
+ = + =
2. Gii bt phng trnh :3 2
4 16
2
20 log 7 log 3 logx x x
x x x+ .
Cu III: (2 im)
1. Tam gic ABC c BC a= ;7
cos8
A = v din tch bng2 15
4
a.Gi , ,
a b ch h h ln lut l di
cc ng cao h t cc nh , ,A B C ca tam gic. Chng minh rng .a b ch h h= +
2. Tm gi tr ln nht ca hm s sin (1 6 cos )2 2
x xy = + .
Cu IV: (3 im)
1. Trn mt phng toOxy cho hai ng thng 1( ) : 2 1 0d x y + = v 2( ) : 2 7 0d x y+ = .
Lp phng trnh ng thng qua gc ta v to vi 1( )d , 2( )d tam gic cn c y thuc ng
thng . Tnh din tch tam gic cn nhn c .
2. Cho hnh lng tr tam gic 1 1 1.ABC AB C c cc mt bn l hnh vung cnh a .Gi D,E,F ln lt
l trung im cc on thng 1 1 1 1, , .BC A C C B Tnh khong cch gia DE v 1A F .
Cu V: (1 im)
Tnh2
0
1 sin
(1 cos ) xx
I dxx e
=
+
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 4-2005:
Cu I:
1. Cc bn c th t gii.
2. Cc bn t chng minh.
Cu II:
1. p s:1 3
( ; ) ( ; )2 2
x y =
2.t 2log x t= . p s:
5
1 1
44 84
10
161 2
x
x
x
x
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2006
THI THI HC, CAO NG S 1Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s 3 22 3 1 y x x= (C)1. Kho st s bin thin v v th ca hm s.2. Gi kd l ng thng i qua M (0;-1) v c h s gc k. Tm kng thng kd ct (C) ti baim phn bit.
Cu II: (3 im)
1. Trong mt phng vi h trc ta vung gc Oxy, cho tam gic ABC c A(1;0), hai ngthng tng ng cha ng cao k t B, C ca tam gic th t c phng trnh: 2 1 0x y + = v3 1 0x y+ = .
Vit phng trnh ng trn ngoi tip tam gic ABC.
2. Tm ta trc tm H ca tam gic ABC trong khng gian Oxyz vi A(3; 0; 0), B(0; 2; 0), C(0; 0;1).
3. Cho hnh chp tam gic u SABC, cnh y l a, cnh bn l b. Tnh khong cch t A n mtphng (SBC).
Cu III: (2 im)
1. Gii phng trnh: 2 25 1 54 12.2 8 0 x x x x + = .
2. Gii phng trnh:2cos4
cot tansin2
xx x
x= +
Cu IV: (2 im)
1. Tnh tch phn:1
20
4 5
3 2
x I dx
x x
+=
+ +
2. Mt trng THPT c 18 hc sinh gii ton din, trong c 7 hc sinh khi 12, 6 hc sinh khi11, 5 hc sinh khi 10. Hi c bao nhiu cch chn 8 hc sinh trong s 18 hc sinh trn i d tri hsao cho mi khi c t nht 1 hc sinh c chn?
Cu V: (1 im)Tm cc gc A, B, C ca tam gic ABC sao cho 2 2 2sin sin sinQ A B C = + t gi tr nh nht.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2006:
Cu I:
1. Cc bn t gii.
2. p s: 9 k 08
k v> .
Cu II:
1. p n: Phng trnh:( 2 236 10 43
07 7 7
x y x y+ + = )
2. p s: H12 18 36
; ;49 49 49
3. p s:
2 2
2 2
3( ; ) 4
a b ad A SBC
b a
=
.
Cu III:
1. p s: 3x = v9
4x =
2. p s:3
x k
= + ( )k Z .
Cu IV:
1. p s:27
ln4
I=
2. p s: ( )8 8 8 818 11 13 12 304351C C C C + + = .
Cu V:
p s: 30oA B= = v 120oC= .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2006
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s:2 3 3
1
x xy
x
+ +=
+(C)
1. Kho st s bin thin v v th ca hm s.2. Chng minh rng qua im M(-3;1) kc 2 tip tuyn ti th (C) sao cho hai tip tuyn vung gc vi nhau.
Cu II: (2 im)
1. Tm m bt phng trnh sau c nghim: 22 1 0. x m x+ + <
2. Tnh tch phn:1
3 1
0
x I e dx
+=
Cu III: (2 im)1. Gii phng trnh: 2log 23 1x x=
2. Gii phng trnh: ( )2 22 1
cos cos sin 13 3 2
x x x
+ + + = +
Cu IV: (2 im)1. Trong mt phng vi h trc ta vung gc Oxy cho parabol (P): 2y x= v im M(1;-1). Gis A, B l hai im phn bit, khc M, thay i trn (P) sao cho MA v MB lun vung gc vinhau. Chng minh rng ng thng AB lun i qua 1 im cnh.
2. Trong khng gian vi h ta vung gc Oxyz cho im A(1; -1; 1) v hai ng thng theo th
t c phng trnh: ( )1 : 1 2
3
x t
d y t
z t
=
= + =
; ( )23 3 0
:2 1 0
x y zd
x y
+ + =
+ =
Chng minh rng ( )1d , ( )2d v A cng nm trong mt mt phng.
Cu V: (2 im)1. C bao nhiu s t nhin chn gm 5 ch si mt khc nhau sao cho trong khng c mt
ch s 2.2. Tm gi tr nh nht ca biu thc
3 3 3
, x y z
Qy z x z x y
= + ++ + +
vix, y, z l cc s dng tha iu
kin: 6 x y z+ + .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2006:
Cu I:
Cc bn t gii.
Cu II:
1.p s: m > -1.
2.p s: I =22
3
e.
Cu III:
1.p s:x = 2.
2.p s:. 26
x k
= + ;5
26
x k
= + ; x k= ( )k Z .
Cu IV:
Cc bn t gii.
Cu V:
1.p s: 1680 + 4410 = 6090.
2. Hng dn: p dng BT Cauchy cho 3 s dng.
Qmin = 6, khix = y = z = 2.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2006
THI THI HC, CAO NG S 3Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
1. Kho st v v th hm s: 3 3 3 y x x= +
2. Tnh o hm cp n ca hm s:2
2004
5 6
xy
x x=
+.
Cu II: (2 im)1. Chng minh rng trong mi tam gic ABC ta lun c :
tan 3 tan 3 tan 33 3 3
A B C
4 tan tan tan 3
3 3 3
A B C = + +
.
2. Gii phng trnh:2 2
2 2
sin sin 22
sin 2 sin
x x
x x+ = .
Cu III: (2 im)
1. Tm gii hn:3
1 3lim .
1 1x x x
2. Tnh tch phn:1 2
20
.4
x dx
x +
Cu IV: (3 im)
1. Cho hai ng thng:1
2
2 4( ) : ,
1 1 18 6 10
( ) : ,2 1 1
x y zd
x y zd
+= =
+ = =
Trong h ta vung gc Oxyz. Lp phng trnh ng thng (d) ct 1( )d , ( )2d v (d) song song
vi trc Ox.
2. Cho t din OABC vi OA = a, OB = b, OC = c v OA, OB, OC i mt vung gc vi nhau.Tnh din tch tam gic ABC theo a, b, c. Gi , , l gc gia OA, OB, OC vi mt phng
(ABC). Chng minh rng: 2 2 2sin sin sin 1. + + = Cu V: (1 im)
Trong mt phng vi h trc ta vung gc Oxy cho parabol (P): 2y x= ta ly A(-1;1), B(3;9).Gi (D) l min phng gii hn bi on AB v (D).
Chng minh rng vi mi M bt k thuc cung nh AB ca (P) th34
ABM
D
S
S , DS l din
tch ca min (D), ABMS l din tch .ABM
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 3-2006:
Cu I:
1. Cc bn t gii.2.p s: ( )
3 22004. 1 ! .
3 2nn
y nx x
=
Cu II:
1. Cc bn t gii.
2.p s:2
32
2 , ,3
x k
x k k Z
= +
= +
Cu III:
1. p s: 1.
2. p s:5 1 5
2ln2 2
I +
=
.
Cu IV:
1. p s:2 2 2 2 2 21 .
2ABCS a b b c c a= + +
2. Cc bn t gii.
Cu V:
Cc bn t gii.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2006
THI THI HC, CAO NG S 4Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s2 2 5
1
x kxy
x
+ =
(k l tham s).
1. Kho st v v th ca hm s (1) vi k=1.
2. Vi gi tr no ca tham s k th hm s c cc i, cc tiu v cc im cc i, cc tiu nm vhai pha ca ng thng (l): 2 0x y = .
Cu II: (2 im)
1. Gii phng trnh: ( )21
2 cos cos3
x x + + 28 1
s in2 3cos sin .3 2 3
x x x
= + + + +
2. Vi gi tr no ca tham skth hm s2
2
1lg 3
1
x kxy
x x
+=
+ + xc nh vi mix.
Cu III: (3 im)
1. Cho hnh chp t gic u S.ABCD c cnh dy bng ng cao v bng a. Tnh khong cchgia hai ng thng SC v AB.
2. Trong khng gian vi h ta Oxyz, cho ng thng ( ) c phng trnh :1 2
2 1 3
x y z = =
v mp(Q) i qua im M(1; 1; 1) v c vectphp tuyn ( )2; 1; 2n =
. Tm ta cc im
thuc( ) sao cho khong cch t mi im n mp(Q) bng 1.
Cu IV: (2 im)
1. Xc nh h s ca s hng cha 4a trong khai trin nh thc Newton2 2
n
aa
(vi 0a ),
bit rng tng cc h s ca 3 s hng u tin trong khai trin bng 97.
2. Tnh tch phn: 2
1
lnln .
1 ln
ex
I x dxx x
= +
+
Cu V: (1 im)Cho a thc: ( ) ( )2f x mx n p x m n p= + + + +
Vi m, n, p l ba s thc tha mn: ( )( ) 0m p m n p+ + + < .
Chng minh rng: ( )2 2 2 2 .n p m m n p np+ > + + +
------------------ HT -------------------
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36/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 4-2006:
Cu I:
1. Cc bn t gii.2.p s 2 2 6 2 2 6k < < +
Cu II:
1. p s ( )22
x k k Z
= +
2. p s: 5 1.k < <
Cu III:
1.p s:2 5
5
ad=
2.p s: ( )1 9; 2;12A ; 2 ( 3;4; 6)A .
Cu IV:
1.p s: ( )
44
8 2 1120.C = 2.p s: ( )
21 2 .
3I e= + +
Cu V:
Cc bn t gii.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
37/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2006
THI THI HC, CAO NG S 5Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s2 1
1x xy
x
+=
(C)
1. Kho st v v th (C) ca hm s.
2. Vit phng trnh ng thng (d) i qua im3
0;2
A
v ct (C) ti hai im phn bit B, C
tha mn: 2 0 AB AC + =
.
Cu II: (2 im)
1. Gii h phng trnh:2 2
3 1 4 2
3
x xy y
x y
+ + = +
+ =
2. Gii bt phng trnh:( ) ( )
4
22
2 10.
log 2 25
xx
x x
+
Cu III: (2,5 im)Cho hnh hp ch nhtABCD.ABCD c th tch bng 1. GiI, J, Kln lt l trung im ca cc onthngAA, CD, AD.
1. Tnh th tch khi t dinBIJK.
2. Bit BK vung gc vi mt phng (ACD). Tnh di cc cnh ca hnh hp.3. Tm gi tr ln nht ca khong cch gia hai ng thng CIvAJ.
Cu IV: (2 im)
1. Tnh cc gc ca tam gic ABC, bit 2A = 3B v 2.a b=
2. Tnh32
4 20
cos.
cos 3cos 3
x I dx
x x
= +
Cu V: (1,5 im)
Trong mt trng hc c 5 em khi 12; 3 em khi 11 v 2 em khi 10 l cc hc sinh xut sc. Hic bao nhiu cch c 5 em hc sinh xut sc ca trng tham gia mt on i biu sao cho mikhi c t nht 1 em?
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
38/66
Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 5-2006:
Cu I:1. Cc bn t gii.
2. p s: ( )
3
.2:5 3
.4 2
yd
y x
=
=
Cu II:
1.p s ( ) ( ) ( ); : 1; 2 & 2;1 .x y
2. p s:
5;
4 0;0 3;
4 5 .
x
xx
x
<
<
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2007
THI THI HC, CAO NG S 1Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
1. Kho st s bin thin v v th hm s
2
1x
y x= (C)2. Tm trn th (C) mt im c hanh ln hn 1 sao cho ti im ny tip tuyn ca (C) tovi 2 ng tim cn ca (C) to thnh 1 tam gic vi chu vi nh nht .
Cu II: (2 im)
Gii cc phng trnh sau :1. ( )2 2 3 3tan tan .sin 1 cos 0 x x x x =
2. ( )232 9 53
xx x
x
+ = +
Cu III: (2 im)
Cho2 2
0
sin2cos 3sin
x I dx
x x
=+
v2 2
0
cos2cos 3sin
x J dx
x x
=+
1. Tnh 9I - 4JvI+J.2. T suy ra kt qu ca I v J .
Cu IV: (2 im)
1. Trn mt phng vi h ta Descartes vung gc Oxy cho 3 ng thng
1 :3 4 4 0d x y = 2 : 6 0d x y+ = 3 : 3 0d x = Tm ta cc nh ca hnh vung ABCD bit rng A,C thuc d3, B thuc d1v D thuc d2 .
2. Cho 1, , ;33
a b c
. Chng minh rng :75
a b c
a b b c c a+ +
+ + +.
Cu V: (2 im)1. Gii phng trnh : 8.27 38.18 57.12 27 0 x x x + =
2. Cho hnh chp tam gic u S.ABC c ng cao SO=1 v y ABC c cnh bng 2 6 . Ccim M, N theo th t l trung im ca cnh AB, AC . Tnh th tch hnh chp S.AMN v bn knhmt cu ni tip hnh chp .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2007:
Cu I:1. Bn t gii2. Gi im M thuc th tha , gi I l giao im 2 tim cn ng . A,B l giao im ca 2 timcn vi tip tuyn . Hy tnh din tch tam gic AIB chng minh tch IA.IB khng i . Sau dng nh l hm cos tnh di AB trong tam gic AB :
2 2 2 2. . .cos 2 . 8 AB IA IB IA IB AIB IA IB= +
p n : 44 4
1 11 ;2 2
2 2M
+ + +
.
Cu II:
1.a v phng trnh tch. p n :
2
4 2 1,cos
2 24
24
x k
x k
k Z
x k
x k
= = + =
= + +
= +
.
2.p n:3
11
x
x
=
=.
Cu III:
1.t tan2
xt= . p n :
9 4 1
1 13 1 13 3ln13 13 1 13 3
I J
I J
=
+ = + +
2. Gii phng trnh cu 1.
Cu IV:
1. Chng minh B v D i xng nhau qua d3 .Sau tm tm hnh vung ABCD l I , dn n hthc (a-2)2=1.p n : A(3;3), B(2;2), C(1;3), D(4;2); A(1;3), B(2;2), C(3;3), D(4;2).
2.p s: ( )1
; ; 3;1;3
a b c
=
v cc hon v.
Cu V:1. Xt hm s: ( ) 8.27 38.18 57.12 27 x x xf x = + . Hy chng minh hm s ny l ng bin.T suy ra phng trnh c nghim duy nht. p s:x=0.
2. p n:1 3 3
. ;3 2 4 2 2
SAMN AMN V SO S r = = =+
.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2007
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s 3 2( 1) ( 1) 1y x m x m x= + + + .1.Kho st s bin v v th hm s khi 1m = .2.Chng t vi mi gi tr khc 0 ca m , th ca hm s ct trc honh ti 3 im phn bit A, BC trong B, C c honh ph thuc tham sm. Tm gi tr ca m cc tip tuyn ti B, C songsong vi nhau.
Cu II: (2 im)1. Gii phng trnh: 23 4sin 2 2cos 2 (1 2sin ) x x x = + .
2. Tm gi tr nh nht v gi tr ln nht ca hm s 3 2( ) 2 3 12 10 f x x x x= + trn [-3; 3].Cu III: (2 im)
Tam gic ABC c cc gc , ,A B C tha mn
sin
sin
sin
sin
2 4sin 1 4sin22
4sin 1 4sin2
A
B
B
C
A B
B C
+ = +
+ = +
.Chng minh tam gic ABC u.
Cu IV: (2 im)
Tnh tch phn3
2
4
tan
cos . 1 cos
x I dx
x x
=+
.
Cu V.A: (2 im) ( Dnh cho THPT khng phn ban)
Hnh chp t gic u SABCD c cnh y AB a= ; chiu cao 62
aSO = . Mt phng ( )P qua A
vung gc vi SC ct , ,SB SC SD ln lt ti ' ' ', , B C D .1. Tnh din tch thit din to thnh v tm t s th tch ca 2 phn hnh chp b ct bi mt phng( )P .
2. Tnh sin ca gc gia ng thng 'AC v mt phng ( )SAB Cu V.B: (2 im) ( Dnh cho THPT phn ban)
1. Tnh gi tr biu thc:5 7 2007
4 5 2008
...
...
i i iP
i i i
+ + +=
+ + +(trong 2 1i = )
2. Trong khng gian vi h trc ta Oxyz, cho tam gic ABC c ( 1; 3; 2)A ; ng cao BK
v trung tuyn CM ln lt nm trn cc ng thng:1
2
1 1 4( ) ;2 3 4
1 2 5( ) .
2 3 1
x y zd
x y zd
+ = =
+ = =
Lp phng trnh ng thng cha cc cnh ,AB ACca tam gic ABC.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2007:
Cu I:1. Bn t gii2.Hanh giao im ca th vi trc honh l nghim pt : 3 2( 1) ( 1) 1 0 x m x m x + + + = T phng trnh trn => pcm .Cng t pt trn ta suy ra c cc h s gc ca tip tuyn ti B,C : ( 2) 1k m x m= + Vix1, x2 phn bit th, tip tuyn ti B v C song song nhau khi v ch khi kB=kcp s :m=2.
Cu II:
1.a v pt tch. p s : ( )
26
72
6
218 35 2
18 3
x k
x k
k Zkx
kx
= +
= +
= + = +
2. Dng o hm kho st .p s : Minf(x)=f(-1)=17; Maxf(x)=f(-3)=35.
Cu III :Hm s 2 4xy x= + ng bin cy(x)=1 x=0 . Ta c :
sin
sin
24sin 1 4sin sin sin2
A
B A B A B+ = + = .
Cu IV:
t 22 tant x= + th2 2
tan
cos 2 tan
xdxdt
x x=
+.
p s:5
3
5 3 I dt = = .
Cu V.A:Cc bn t gii.
Cu V.B:
1.p s:P=0.2. p n:
Phng trnh AB :1 3 2
2 9 7
x y z+ + = = . Phng trnh AC:
1 3 2
13 19 8
x y z+ + = =
.
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2007
THI THI HC, CAO NG S 3Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)Cho hm s 3 2 2 2(2 3) (2 9) 2 3 7( )my x m x m m x m m C = + + + +
1. Kho st hm s khi 0m = 2. Tm m ( )mC ct trc honh ti 3 im phn bit c honh 1 2 3, ,x x x khng nh hn 1.
Cu II: (2 im)Gii cc phng trnh sau:
1. 3 3 x x+ + = ;2. 2cos cos 2 cos3 5 7cos 2 . x x x x+ =
Cu III: (2 im)Trong khng gian vi h trc ta Oxyz cho mt phng ( )P c phng trnh 3 0 x y z+ + + = vcc im (3;1;1); (7;3;9); (2;2;2) A B C .1. Tnh khong cch t gc ta n mt phng ( )ABC .
2. Tm M thuc mt phng ( )P sao cho 2 3 MA MB MC + +
nh nht.
Cu IV: (2 im)
1. Tnh1 3
2 30 (1 )
x I dx
x=
+ .
2. Cho cc s dng , , x y z tha mn:
2 2
2 2
2 2
3 3 75
3 2716
x xy y
y z
z xz x
+ + =
+ =
+ + =
. Tnh 2 3P xy yz xz= + + .
Cu V.A: (2 im) ( Dnh cho THPT khng phn ban)
1. Trong mt phng ta Oxyz , hy lp phng trnh ng thng dcch im (1;1)A mkhong bng 2 v cch (2;3)B mt khong bng 4.
2. Cho dy s ( )nu c s hng tng qut3
5
195(1 )
16( 1)
nnn
n n
Cu C n
n
++
= +
. Tm cc s hng dng ca
dy.
Cu V.B: (2 im) ( Dnh cho THPT phn ban)1. Gii phng trnh trong tp hp s phc 2 0z z+ = .
2. Cho hnh chp t gic u .S ABCD c cnh y bng a v ASB = . Tm th tch hnh chp.S ABCD .
------------------ HT -------------------
8/2/2019 Tuyen Tap Cac de Thi Thu Dai Hoc Cao Dang Tren Tap Chi Toan Hoc Tuoi Tre
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 3-2007:
Cu I:
1.Bn t
gii
2. PT hanh giao im c dng : ( ) ( )( )2 21 2 1 2 3 7 0 x x m x m m + + + = . Sau xt tip phng trnh bc 2 c 2 nghim phn bit ln hn 1.p s: 2 < m < 3.
Cu II:
1.t ( )3 3u x u= + . Ta a vc hi xng nh sau :3
3
u x
x u
=
= .
Gii h trn kt hp vi iu kin suy ra nghim .
p s: 7 132
x+
= .
2.a v phng trnh tch .p s: ( ) x k k Z = .
Cu III:
1. Vit phng trnh mt phng (ABC) . Sau dng cng thc khang cch tnh khang cch .
p s : ( )( )2 6
,3
d O mp ABC =
2. Chn im I sao cho: ( )2 3 0 4 IA IB IC + + =
Khi 2 3 MA MB MC + +
min khi MI
min hay M l hnh chiu ca I ln mp(P) .
T (4) ta tm c23 13 25
; ;6 6 6
I
.
Sau tm hnh giao im ca (d) qua I v vung gc mp(P)
p s :5 20 2
; ;9 9 9
M
Cu IV:
1.t ( )2tan tan 1 x dx d = = +
( )( )
34 43
220 0
tan . 1cos cos (cos )
161 tan
dJ d
= = + =
+
p s :1
16J = .
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
2. ( )
( )
2 2
2 2
2 2
3 3 75
3 27 5
16 6
x xy y
y z
z xy x
+ + =
+ =
+ + =
Bi ny kh r
i. Ta s
biu di
nx, y
quaz
.t x = kz . Ta c : ( ) ( ) ( )2 2 2 2 2 23 3 3 3 0 z xy x y z x xy y+ + + + + + =
2 22 1 z xz xy y zk
+ = = +
T (5) v (6) suy ra hng cp :
( )
22
2 2
21 3 27
1 16
zk
z k k
+ + =
+ + =
.
Gii ra gi tr ca kvz .p s: 24 3P = .
Cu V.A:Cc bn t gii.
Cu V.B:
1.t z = x+yi. p s: z1 = 0; z2 = i; z3 = -i.
2. Gi O l tm hnh vung ABCD . I l trung im AB. Tnh SO.
p s:3
.
. cos
6.sin2
S ABCD
aV
= .
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2007
THI THI HC, CAO NG S 4Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s( )2 2 3 6 1
2 x m x m
y x
+
= (1)1. Kho st v v th hm s khi (1) khi m=1 .2. Tm m hm s (1) c cc i , cc tiu ng thi 2 im cc i v cc tiu nm v 2 phaca ng thng y = -x + 7.
Cu II: (2 im)
1. Gii phng trnh : 3 3sin cos cos2 .tan .tan4 4
x x x x x
= +
2. Gii h phng trnh :( )
( )
3 2
3 2
1 2
1 2
x x x y
y y y x
+ = +
+ = +
.
Cu III: (2 im)
Trong khng gian Oxyz , cho 2 im A(1 ; -1; 2) , B(3; 1; 0) v mt phng (P) c phng trnh (P) cphng trnhx 2y - 4z +8 = 0 .1. Lp phng trnh ng thng (d) tha mn ng thi cc iu kin sau : (d) nm trong mtphng (P) , (d) vung gc vi AB v (d) i qua giao im ca ng thng AB vi mt phng (P)2. Tm ta C trong mt phng (P) sao cho CA=CB v mt phng (ABC) vung gc vi mt phng(P).
Cu IV: (2 im)
1. Tnh tch phn :1
2
0
3 6 1 I x x dx= + +
2. Chng minh rng:2 21 2 7 2 1 2 7 x xy y + + . Vix, y l cc s thc tha mn 2 2 3 x xy y + .
Cu V: (2 im)1. Gii phng trnh :
( ) ( )5 4log 3 3 1 log 3 1x x+ + = + .
2. Cho hnh chp tam gic u S.ABC c ng cao SH=h ,
ASB = .Tnh th tch hnh chp theo h v .
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 4-2007:
Cu I:
1. Bn t gii
2 Hm s c cc i cc tiu khi( )
2
24 10 7'
2
x x my
x
+ =
= c 2 nghim phn bit .
Gi ta 2 im cc i , cc tiu l C(x1;y1) , CT(x2;y2) .
Dng iu kin khc pha xt du .
p s :41 3 229 41 3 229
4 4m
+< < .
Cu II:
1. Dng gc cung lin kt a v pt tch.
p s : ( )2 ; 22
x k x k k Z
= + = .
2.a v hm s ( ) 3 22 2 1 f t t t t = + + . Sau chng minh hm s lun ng bin .
Nux>y th 2y=f(x)>f(y)=2x . V l . Tng t=> x = y .
p s :1 5
1;2
x x
= = .
Cu III:
1.p n : ( )2 3
: 2 1 1
x y zd
+ = = .
2.p s : C(2 ;1 ;2).
Cu IV:
1. ( )( )1
2
0
4 3 1 I x dx=
t2
1 sin , ;
2 23
x t t
=
. Khi ( )0
3
21 cos 2
3
I t dt
= + .
p s :2 1
23 3I
= +
2. Cc bn t gii .
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
Cu V:
1.t ( ) ( )5 4log 3 3 1 log 3 1x x t+ + = + =
Ta c ( )3 1 4
3 2 5 33 3 1 5
x t
t tx t
+ = + = + + =
T (3) ta c1 2
3. 15 5
t t
+ =
. V tri nghch bin .
p s :x=1.
2. p s :3
2
3
3.cot 12
hV
=
.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2008
THI THI HC, CAO NG S 1Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho h th:
2 2 1( ) 1
x x mCm x
+ + = .
1. Kho st v v th hm sng vi m = 1.2. Tm m (Cm)c cc im cc i, im cc tiu v gc ta O lp thnh tam gic vung ti O
Cu II: (2 im)1. Gii phng trnh:
sin(3 ) sin 2 .sin( ).4 4
x x x
= +
2. Gii h phng trnh:
2 2 2
3 3 3
.log 3 log log
.log 12 log log
x y y x
x x y y
+ = +
+ = + .Cu III: (2 im)
1. Tnh cc tch phn sau:
2
31 . 1
dxI
x x=
+ ;
2
40
sin2
1 cos
x J dx
x
=+
.
2. Cho bn imA(5;1;3),B(1;6;2) , C(5;0;4) ,D(4;0;6). Chng minh rng hai ng thngAB vCD cho nhau. Tnh khong cch giaAB v CD v vit phng trnh ng vung gc chung cachng.
Cu IV: (2 im)
1. Gii phng trnh:32( 2)( 4 4 2 2) 3 1 x x x x + = .2. Cho a, b l cc s thc dng. Chng minh rng :
2 2
2 3
(1 )(1 )2 .
( 1)(1 )
a b b
a a b
+ +
+ +
Cu V.A: (2 im) ( Dnh cho THPT khng phn ban)1. Cho n l s nguyn dng vi n 2. Chng minh rng:
2 1 2 2 2 3 2 21 . 2 . 3 . ... . ( 1).2n nn n n nC C C n C n n
+ + + + = + 2. Cho tam gicABC. Xt tp hp gm nm ng thng song song viAB; su ng thng songsong viBCv by ng thng song song vi CA. Hi cc ng thng ny to ra bao nhiu hnh
bnh hnh, bao nhiu hnh thang?Cu V.B: (2 im) ( Dnh cho THPT phn ban)
Cho ng thng () c phng trnh 2 2 0x y + = v elip (E) c phng trnh2 2
18 4
x y+ = . Gi
sng thng () ct (E) ti hai imB v C.1. Tm im A thuc elip (E) tam gicABCcn ti A.2. Tm im A thuc elip (E) din tch tam gicABCt gi tr ln nht.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2008:
Cu I:1. Cc bn t gii.2. (Cm) c im cc i M v im cc tiu N khi v ch khi m > - 2.
S dng iu kin ,0. =ONOM ta tm c5
7=m .
Cu II.
1. p s:24
kx = .
2. p s: ( ) .2log2;2log;3
4
3
4
=yx
Cu III.
1. p s:
+=
2
223ln
3
1I ;
4
=J .
2. p s:103
23693=IJ
Phng trnh ng vung gc chung:144
103
476
1221103
586
==
zy
x
.
Cu IV:1. p s:x = 32. Cc bn t chng minh.
Cu V.A:1. Cc bn t chng minh.2. p s: S hnh bnh hnh l: 675 ( hnh ). S hnh thang l: 1575 (hnh).
Cu V.B:
1. p s:
+
+
25
3921;
5
392,
25
3921;
5
39221 AA
2. p s: ( )2;2 A
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2008
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s: 4 2 2( ) : 2( ) 5 5Cm y x m x m m= + + + 1. Kho st s bin thin v v th (C1) ca hm s khi m = 1.2. Vi nhng gi tr no ca m th th (Cm) c im cc i v im cc tiu, ng thi cc imcc i v im cc tiu lp thnh mt tam gic u.
Cu II: (2 im)
1. Gii phng trnh:1
(1 cos )(1 cos 2 )(1 cos3 ) .2
x x x+ + + =
2. Gii h phng trnh:2
1 2
1 2
2log ( 2 2) log ( 2 1) 6
log ( 5) log ( 4) 1
x y
x y
xy x y x x
y x
+
+
+ + + + =
+ + =
Cu III: (2 im)
1. Tnh tch phn:
11 3 3
41
3
( ).
x x I dx
x
=
2. Cho cc s thc dng a, b, c tha mn ab + bc + cd= abc. Chng minh rng:4 4 4 4 4 4
3 3 3 3 3 31.
( ) ( ) ( )
a b b c c a
ab a b bc b c ca c a
+ + ++ +
+ + +
Cu IV: (2 im)Trong khng gian vi h ta Descartes Oxyz, cho mt phng (P) c phng trnh
2 1 0 x y z+ + = v ng thng (d) c phng trnh
2 2 0
2 2 0
x y
y z
=
+ + = .1. Tm to giao imA ca (d) v (P). Tnh so gc to bi (d) v (P).2. Vit phong trnh ng thng () i quaA, () nm trong mt phng (P) sao cho gc to bi haing thng () v (d) bng 450.
Cu V.A: (2 im) ( Dnh cho THPT khng phn ban)1. Vit phng trnh ng trn i qua hai imA(2;5) ,B(4;1) v tip xc vi ng thng cphng trnh 3 9 0.x y + = 2. Vi n l s nguyn dng, chng minh h thc sau:
1 2 2 2 22( ) 2( ) ... ( )
2
n n
n n n n
nC C n C C + + + =
Cu V.B: (2 im) ( Dnh cho THPT phn ban)
1.Gii phng trnh: 84 221 1
log ( 3) log ( 1) log 4 .2 4
x x x+ + =
2.Cho hnh chp t gic u S.ABCD c cnh y bng a, chiu cao cng bng a. GiE, K ln ltl trung im ca cc cnhAD vBC. Tnh bn knh ca mt cu ngoi tip hnh chp S.EBK.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2008:
Cu I.1. Cc bn t gii.2.
k
(Cm) c ba
im c
c tr
l
m
< 2. Ccim c
c tr
ca (C
m
) l( ) ( ) ( ).1;2,1;2,55;0 2 mmCmmBmmA + p s: 3 32 =m .
Cu II.
1. p s:
23
2;
24mxkx +=+= .
2. p s: ( ) ( )1;2; =yx .
Cu III.
1. p s: 6=
I 2. Cc bn t gii.
Cu IV.1. p s: ( )1;0;1 A . Gc ( ) 030)(, =Pd .
2. p s: Hai ng thng tho mn l: ( )335
1
3132
1:1
+=
+=
+
zzx;
( )335
1
3132
1:2
+
+=
=
zyx
Cu V.A:
1. p s:2 2
1
2 22
( ) : ( 1) ( 2) 10( ) : ( 17) ( 10) 250C x y
C x y + =
+ =.
2. Cc bn t chng minh.
Cu V.B:
1. p s:3
3 2 3
x
x
=
= +.
2. p s:8
29aR =
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2008
THI THI HC, CAO NG S 3Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s
2
( ) : 1
x
C y x
= 1. Kho st v v th (C) ca hm s.2. Tm cc gi tr ca tham sang thng (d) :y = a(x 3) ct th (C) ti hai im phnbit trong c t nht mt giao im c honh ln hn 1.
Cu II: (2 im)1. Gii phng trnh: 5 3 22sin 2sin .cos cos 2 sin 0 x x x x x+ + =
2. Gii h bt phng trnh:3 2
4 3 2
3 9 10 0
5 5 5 4 0
x x x
x x x x
+ +
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 3-2008:
Cu I.1. Cc bn t gii.2. p s: 0a .
Cu II.
1. p s:
kx
kx
+=
+=
4
22 .
2. p s: 14
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2008
THI THI HC, CAO NG S 4Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s: ( )3 22 1 y x x m x m= + (1).
1. Kho st s bin thin v v th ca hm s khi m = 1.2. Trong trng hp hm s (1) ng bin trong tp s thc R, tm m din tch hnh phng giihn bi th ca hm s (1) v hai trc Ox, Oy c din tch bng 1.
Cu II: (2 im)1. Gii phng trnh nghim thc: 1 tan . tan 2 cos 3 . x x x =
2. Tm tt c cc gi tr ca tham sk phng trnh ( )1 4 2 1 2 x x xk k+ + = c nghim.
Cu III: (2 im)1. Trong mt phng vi h ta Oxy cho elip (E): 2 24 4.x y+ = Qua im M(1;2) k hai ngthng ln lt tip xc vi (E) ti A v B. Lp phng trnh ng thng i qua hai im A v B.
2. Cho tam gic ABC tha mn: ( )5
cos 2 3 cos 2 cos 2 0.2
A B C + + + =
Tnh ln ba gc ca tam gic .
Cu IV: (2 im)
1. Tnh tch phn sau:2
2 sin
0
2cos cos .2
xx I x x e dx
= +
2. Cho ba s thc dngx, y, z tha mn iu kin: 2 1. xy xz+ =
Tm gi tr nh nht ca biu thc:3 4 5
. yz zx xy
S x y z
= + +
Cu V.A: (2 im) ( Dnh cho THPT khng phn ban)1. Trong khng gian vi h trc ta Oxyz cho hai ng thng:
( )12 4 0
:3 0
x yd
z
+ =
= ( )2
0:
1 0
y zd
x
+ =
=
Lp phng trnh mt cu c bn knh nh nht tip xc vi c hai ng thng trn.2. C tt c bao nhiu s t nhin chn c 4 ch s, sao cho trong mi sng sau ln hn ch sng lin trc n?
Cu V.B: (2 im) ( Dnh cho THPT phn ban)1. Cho hnh chp t gic S.ABCD. y ABCD l hnh vung cnh bng a, SA vung gc vi mtphng (ABCD) v SA = a. Tnh din tch ca thit din to bi hnh chp vi mt phng qua Avung gc vi cnh SC.2. Gii bt phng trnh: 2 1log 3 log 2xx .
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 4-2008:
Cu I:1. Cc bn tgii.
2. p s: 316
=m .
Cu II:
1. Hng dn:
=
=
1cos
03cos
x
x.
2. p s:2
10
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2009
THI THI HC, CAO NG S 1Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
1. Kho st v v th ca hm s:
2
( ).1
x
y Cx
= 2. Chng minh rng vi mi gi tr thc ca m, ng thng y x m= + (d) lun ct th (C) tihai im phn bit A, B. Tm gi tr nh nht ca di on thng AB.
Cu II: (2 im)
1. Gii phng trnh2
2 13 .2 6x
x x = .
2. Gii phng trnh tan tan s in3 sin s in26 3
x x x x x
+ = +
.
Cu III: (1 im)Tnh th tch hnh chp S.ABCbit , , , 60 ,oSA a SB b SC c ASB= = = = 90 , 120 .o o BSC CSA= =
Cu IV: (1 im)
Tnh tch phn( )
2
30
sin .
sin 3.cos
x dxI
x x
=
+ .
Cu V: (1 im)
Tm gi tr nh nht ca biu thc 2 2 22 2 2log 1 log 1 log 4P x y z= + + + + + trong l cc s
dng , , x y z tha mn iu kin 8.xyz =
PHN DNH RING CHO CHNG TRNHCHUN.
Cu VIa: (2 im)1. Trong mt phng vi h trc ta vung gc Oxy, cho hai ng thng c phng trnh
11 0( ); x y d + + = 22 1 0( ). x y d = Lp phng trnh ng thng i qua im (1; 1)M ct 1( )d ,
2( )d tng ng ti A, B sao cho 2 0 MA MB+ =
.
2. Trong khng gian vi h trc ta vung gc Oxyz, cho mt phng (P) c phng trnh2 2 1 0 x y z+ + = v hai im (1: 7 : 1)A , (4;2;0)B . Lp phng trnh ng thng (d) l hnh
chiu vung gc ca ng thng AB trn mt phng (P).
Cu VIIa: (1 im)K hiu 1x , 2x l hai nghim phc ca phng trnh bc hai
22 2 1 0x x + = . Tnh gic tr cc s
phc21
1
x,
22
1.
x
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
PHN DNH RING CHO CHNG TRNH NNG CAO.
Cu VIb: (2 im)1. Trong mt phng vi h trc ta vung gc Oxy, cho hyperbol (H) c phng trnh
2 2
19 4
x y
= . Gi s (d) l mt tip tuyn thay i v F l mt tring hai tiu im ca (H), k FMvung gc vi (d). Chng minh rng M lun nm trn mt ng trn cnh, vit phng trnhng trn .2. Trong khng gian vi h truc tc vung gc Oxyz, cho ba im (1;0;0)A , (0;2;0)B , (0;0;3)C .Tm ta trc tm ca tam gic ABC.
Cu VIIb: (1 im)Ngi ta s dng 5 cun sch Ton, 6 cun sch L, 7 cun sch Ha (cc cun sch cng loiging nhau) lm gii thng cho 9 hc sinh, mi hc sinh c hai cun sch khc loi. Trong s9 hc sinh trn c 2 bn Ngc v Tho. Tm xc sut hai bn Ngc v Tho c gii thng gingnhau.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 1-2009:
Cu I:1. Cc bn t gii.
2. p s: min 2 2AB = 2m = .
Cu II:
1. Phng trnh c 3 nghim: p s:3
1
1 1 8log 6
4
x
x
= +
=
.
2. Phng trnh c 3 h nghim: p s:22
23
x k
x k
x k
=
=
= +
.
Cu III:
p s: Th tch l2
12V abc= .
Cu IV:
p s:3
6I= .
Cu V:
p s: min 5 2 2P x y z= = = = .
Cu VI.a:1. p s:ng thng:x=1.
2. Phng trnh ng thng:3 2
4 3 1
x y z = =
.
Cu VII.a:p s: Cc gi tr: (-2i; 2i).
Cu VI.b:Cc bn t gii.
Cu VII.b:Cc bn t gii.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2009
THI THI HC, CAO NG S 2Mn thi: TON
Thi gian lm bi: 180 phtCu I: (2 im)
Cho hm s )(1
42Cx
x
y +
= .1. Kho st s bin v v th hm s(C).2. Tm trn th (C) hai im i xng nhau qua ng thng MN bit M (-3;0) v N (-1;-1).
Cu II: (2 im)
1. Gii phng trnh: .2
7
4
3cos4cos
2
12coscos4 4 =+
xxxx
2. Gii phng trnh: 1232.3 ++= xx xx .
Cu III: (1 im)
Tnh tch phn:
+
+=
2
0 cos1
sin1
dxex
xI
x .
Cu IV: (1 im)Cho hnh chp tam gic u S.ABC di cnh bn bng 1. Cc mt bn hp vi mt phng y mtgc . Tnh th tch hnh cu ni tip hnh chp S.ABC.
Cu V: (1 im)Trong khng gian vi h ta vung gc Oxyz cho ng thng l c phng trnh:
)(
24
2
32
Rt
tz
ty
tx
+=
=
+=
v hai im A(1;2;-1), B(7;-2;3).
Tm trn ng thng l nhng im sao cho tng khong cch t n A v B l nh nht.
PHN DNH RING CHO CHNG TRNHCHUN.
Cu VIa: (2 im)1. Nm on thngc di 1 cm, 3 cm, 5 cm, 7 cm, 9cm. ly ngu nhin ba on thng trong nmon thng trn. Tm xc sut ba ton thng ly ra lp thnh mt tam gic.
2. Gii h phng trnh:
=
+=
5
8
yx
yyxyxx
.
Cu VIIa: (1 im)
Tm gi tr nh nht ca hm s:)sincos2(sin
cos2
xxx
xy
= , vi .
30
< x
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
PHN DNH RING CHO CHNG TRNH NNG CAO.
Cu VIb: (2 im)
1. Tm cc gi tr cax trong khai trin khai nh thc Newton:n
xx
+ 5 3log)2()310log( 22 bit rng
s hng th su ca khai trin bng 21 v 231 2 nnn CCC =+ .
2. Cho
+=
3
2sin
3
2cos3
i . Tm cc s phc sao cho =3 .
Cu VIIb: (1 im)Gi a, b, c l di ba cnh ca mt tam gic c chu vi bng 2. Chng minh rng:
2227
52 222
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 2-2009:
Cu I:1. Cc bn t gii.2.p s: (0; 4); (2; 0)A B .
Cu II:1. p s: 8kx = .2. Phng trnh c 2 nghim: p s: 1;1 == xx .
Cu III:
p s: 2
eI = .
Cu IV:
p s:
3
2
sin tan
tan 4(1 sin )V
= + + .
Cu V:p s: (2;0;4)M .
Cu VI.a:
1. p s:35
3
C.
2. p s: )2;3();2;3();( =yx .
Cu VII.a:
p s: 13tan2
32min =
+= y .
Cu VI.b:1. p s:x=2.
2.
p s:
+
=
+
=
+
=
9
8sin
9
8cos3
9
2
sin9
2
cos3
9
4sin
9
4cos3
33
3
2
31
i
i
i
.
Cu VII.b:Cc bn t gii.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
B GIO DC V O TOTP CH TON HC V TUI TR
NM2009
THI THI HC, CAO NG S 3Mn thi: TON
Thi gian lm bi: 180 pht
Cu I: (2 im)
Cho hm s )1(1
)12( 2
= x
mxmy .
1. Kho st s bin v v th (C) ca hm s (1) ng vi m = -1.2. Tm m th ca hm s (1) tip xc vi ng thng y =x.
Cu II: (2 im)
1. Gii phng trnh: 09
log))9((log 22 =+
++x
xxx .
2. Gii h phng trnh:
=+
=+
++
yxyx
yx
xyyx
2
22 12
.
Cu III: (1 im)
1. Tm gii hn:3 22
2
0 1
)1ln(lim
2
xe
xL
xx +
+=
.
2. Tnh tch phn: +
=2
03)cos(sin
sin
dxxx
xdxI .
Cu IV: (1 im)
Cho hnh chp ct tam gic u ngoi tip mt hnh cu bn knh rcho trc. Tnh th tch hnhchp ct, bit rng cnh y ln gp i cnh y nh.
Cu V: (1 im)
Cho phng trnh: mxxx
x+=
12
12
13 2( vi m l tham s).
Tm m phng trnh cho c nghim duy nht.
PHN DNH RING CHO CHNG TRNHCHUN.
Cu VIa: (2 im)1. Trong khng gian vi h ta Oxyz cho mt phng P c phng trnh:x+y+z+3=0; ng thng
dc phng trnh:12
2
1
1 zyx=
=
+v cc im A(3;1;1); B(7;3;9); C(2;2;2).
a. Vit phng trnh mt phng (Q) cha dv song song vi mt phng (P).
b. Tm ta ca im M thuc (P) sao cho MCMBMA 32 ++ nh nht.
2. Cho ng trn (C): 012622 =++ yxyx . Vit phng trnh ng thng di qua M(0;2) vct (C) theo mt dy cung c di l 4.
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
Cu VIIa: (1 im)Chng minh rng vi mi s t nhin n ( vi n>2), ta c: )1(22 )1()2( > nnn nnn .
PHN DNH RING CHO CHNG TRNH NNG CAO.
Cu VIb: (2 im)1. Trong khng gian h ta Oxyz cho mt phng ( ) c phng trnh: 3x+2y-z+4=0 v hai imA(4;0;0) v B(0;4;0). Gi I l trung im ca on thng AB. Tm ta giao im ca ng thngAB vi mt phng ( ) v xc nh ta im K sao cho KI vung gc vi mt phng ( ), ngthi K cch u gc ta O av2 mt phng ( ).
2. Cho elip (E) c phng trnh 125100
22
=+yx
. Tm cc im M thuc (E) nhn hai tiu im ca elip
(E) di mt gc 1200.
Cu VIIb: (1 im)
Chng minh rng vi mi s t nhin n ( vi n>2), ta c: )1ln()1ln(ln2
+> nnn .
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Tp th lp 12T THPT Th x Cao Lnh Nin kho 2006-2009 GVCN: Thy Nguynnh Huy
P S HOC HNG DN GIIS 3-2009:
Cu I:1. Cc bn t gii.2. p s: { }1\Rm .
Cu II:1. p s: 10=x .2. H phng trnh c 2 nghim: p s: )3;2();0;1();( =yx .
Cu III:
1. p s:3
7L
= .
2. p s:1
2I = .
Cu IV:Cc bn t gii.
Cu V:p s: Rm .
Cu VI.a:1.a. p s: 01 =++ zyx .
b. p s:
9
2;
9
20;
9
5M .
2. p s: 22;22
1+=+= xyxy .
Cu VII.a:Cc bn t gii.
Cu VI.b:
1. p s: Giao im: )0;16;12( ;
4
3;
2
1;
4
1K .
2. p s:
3150;
33101M ;
3150;
33102M ;
3150;
33103M v
3150;
33104M .
Cu VII.b:Cc bn t gii.
------------------ HT -------------------
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Tuyn tp cc thi thi hc, cao ng trn tp chTon hc v Tui trqua cc nm
Thc hin:
Tp th Lp 12T
Trng THPT Th x Cao LnhNin kha: 2006 -2009
Gio vin ch nhim:
Thy Nguyn nh Huy
1. Tuyn tp cc nm 2003:Tp tht4. Chu trch nhim chnh: L Ngc c
2. Tuyn tp cc nm 2004:Tp tht5. Chu trch nhim chnh: Phm Ngc Trng
3. Tuyn tp cc nm 2005:Tp tht6. Chu trch nhim chnh: L Thanh Sang
4. Tuyn tp cc nm 2006:Tp tht3. Chu trch nhim chnh: Trnh Hong Anh
5. Tuyn tp cc nm 2007:Tp tht2. Chu trch nhim chnh: Nguyn Hong Vit Khnh
6. Tuyn tp cc nm 2008:Tp tht1. Chu trch nhim chnh: Nguyn Hng Hong
7. Tuyn tp cc nm 2009:Tp tht3. Chu trch nhim chnh: Nguyn c Tun
Nguyn c Tun