tuyỂn tẬp cÁc ĐỀ thi thỬ ĐẠi hỌc trÊn bÁo toÁn hỌc tuỔi trẺ
TRANSCRIPT
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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
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 ----
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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
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 .
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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=
=
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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
< 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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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
=
.
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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.
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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
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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.
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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 =
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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 .
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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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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.
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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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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