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7/21/2019 [DeTHiThuDH.net]-De Thi Thu THPT Quoc Gia Lan 1 Truong Ly Tu Trong Khanh Hoa
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SGD & T KHNH HOTRNG THPT L TTRNG
THI THI HC LN I - NM HC 2014-2015Mn: TON
Thi gian lm bi: 180 pht khng kthi gian giao
Cu I: (2) Cho hm s2 1
( )1
xy f x
x
= =
1. Kho st sbin thin v vth(C) ca hm s.2. Gi I l giao im ca hai ng tim cn ca th(C) , hy tm trn th(C) im M c
honh dng sao cho tip tuyn vi th(C) ti im M ct ng tim cn ng , tim cnngang ln lt ti A v B tha mn: 2IA2+ IB2= 12 .
Cu II: (2) Gii cc phng trnh sau :
1.(1 s inx)(2sin 2 6 cosx 2sinx 3)
22cos 1
x
x
+ + +=
+
2. 3 227 3 31log log ( 4) log ( 2)4x x x+ + =
Cu III: (1) Tnh tch phn :1 2
0
( )
2
x
x
x x eI dx
x e
+=
+
Cu IV: (1) Trong mt phng vi hta Oxy ,cho hai im A(1;2); B(4;1) v ng thngd: 3x-4y+5=0. Vit phng trnh ng trn (C) i qua A,B v ct d ti C, D sao cho CD = 6.
Cu V: (1) Trong mt chic hp c cha 6 vin bi , 5 vin bi vng v 4 vin bi trng. Lyngu nhin trong hp ra 4 vin bi. Tnh xc sut trong 4 vin bi ly ra khng c c3 mu.
Cu VI: (1) Cho hnh chp u S.ABCD c di cnh y bng a, mt bn ca hnh chp tovi mt y mt gc 600. Mp(P) cha AB v i qua trng tm G ca SAC ct SC , SD ln ltti M,N . Tnh thtch khi chp S.ABMN theo a
Cu VII: (1) Gii hphng trnh :3 2 3
3 2
6 13 10
2 5 3 3 10 6
x x x y y
x y x y x x y
+ = + +
+ + = +
Cu VIII: (1) Cho 0,, zyx v 3=++ zyx .Tm gi trnhnht ca biu thc:
xzzyyxP
+++
+++
++=
)1ln(24
1
)1ln(24
1
)1ln(24
1
-----------------HT ---------------
7/21/2019 [DeTHiThuDH.net]-De Thi Thu THPT Quoc Gia Lan 1 Truong Ly Tu Trong Khanh Hoa
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Trang 1
P N MN TON THI THLN I NM HC 2014-2015 - KHI 12Cu p n im
1. Kho st sbin thin v vth(C) : 2 1( )1
xy f x
x
= =
: (1)
+ Tp xc nh : D = R \ {1}
+( )
2
1' 0;
1y x D
x
= <
: Hm snghch bin trn cc khong ( ;1)
v (1; )+
0.25
+1 1
lim ; limx x
y y +
= = + : TC x = 1
+ lim 2x
y+
= : TCN y = 2 0.25
+ Bng bin thin:x - 1 + y' - -y 2 +
- 2
0.25
+ im c bit : (0;1) ;1
;02
+ th:
2
1
I
1
0.25
2. (1)
+ I(1;2) . Gi M(x0; 0
0
2 1
1
x
x
) (C) , x0> 0 ; 0 1x
+ Pttt vi (C) ti M : 002
0 0
2 11: ( )
( 1) 1
xd y x x
x x
= +
0.25
+ A l giao im ca d v TC A(1; 00
2)
1
x
x
+ B l giao im ca d v TCN B(2x0-1; 2)0.25
+ Tnh c IA2=
( )
2
0
4
1x
; IB2= 4(x0 1)2
+ 2IA2+ IB2= 12 2 4 20 0 02
0
2( 1) 3 ( 1) 3( 1) 2 0
( 1) x x x
x+ = + =
0 0
20 00
20 00
0 0
1 1 2
1 1 0 (loai)( 1) 1
1 2 1 2( 1) 2
1 2 1 2 (loai)
x x
x xx
x xx
x x
= =
= = = = = + =
= =
0.25
Cu I(2)
+ KL: Vy c 2 im cn tm: M1(2;3) ; M2(1+ 2 ; 2+2
2) 0.25
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Trang 2
1. Gii phng trnh: (1 s inx)(2sin 2 6cosx 2sinx 3) 22cos 1
x
x
+ + +=
+(1)
+ iu kin: 1 2cos 2 ;2 3
x x k k Z
+
+
0.25
(1) (1 s inx)(4sin cos 6cos 2sin 3) 22cos 1
x x x x
x
+ + + =
+
(1 s inx)(2 sin 3)(2 cosx 1)2
2cos 1
x
x
+ + =
+ 0.25
(1 s inx)(2sin 3) 2x + = 22sin sinx 1 0x + = 0.25
22
sinx 121
6sinx2 5
26
x k
x k
x k
= +=
= + = = +
tha mn iu kin
0.25
2. Gii phng trnh: 3 227 3 31
log log ( 4) log ( 2)4
x x x+ + = (1)
+ K : 0 2x< Vi K trn, (1) 3 3 3log log ( 4) log 2x x x + + =
[ ]3 3log ( 4) log 2x x x + = ( 4) 2x x x + =
0.25
2
( 4) 2
2
( 4) 2
x
x x x
x
x x x
>
+ =
+ + =
= = =
7/21/2019 [DeTHiThuDH.net]-De Thi Thu THPT Quoc Gia Lan 1 Truong Ly Tu Trong Khanh Hoa
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Trang 3
C
D
D
O
I
B
I
Nhn xt A thuc d nn A trng vi C hay D . (GisA trng C)Gi I(a;b) l tm ng trn (C), bn knh R>0.(C) i qua A,B nn IA=IB=R
2 2 2 2(1 ) (2 ) (4 ) (1 )a b a b R + = + = 3 6b a =
0.25
Suy ra I(a;3a-6) v R = 210 50 65a a + (1)
Gi H l trung im CD IH CD v IH = d(I;d) =9 29
5
a +
R=IC= ( )2
2 2 9 29925
aCH IH
+ = + (2)
0.25
T(1) v (2) , c:2
10 50 65a a + =
( )2
9 29
9 25
a
+
2
113 56 43 0 43
13
a
a aa
= + = =
0.25
Cu IV(1)
+ a=1 (1; 3); 5I R = . Pt ng trn (C): (x-1)2+(y+3)2=25
+43
13a = 43 51 5 61( ; );
13 13 13I R = .
Pt ng trn (C):2 2
43 51 1525
13 13 169x y
+ =
0.25
Scch chn 4 vin bi bt ktrong hp : 415 1365C = cch 0.25
+ Chn 2 bi , 1 bi trng , 1 bi vng: 2 1 16 5 4. .C C C
+ Chn 1 bi , 2 bi trng , 1 bi vng: 1 2 16 5 4. .C C C
+Chn 1 bi , 1 bi trng , 2 bi vng: 1 1 26 5 4. .C C C
Scch chn 4 vin bi c 3 mu :2 1 16 5 4. .C C C +
1 2 16 5 4. .C C C +
1 1 26 5 4. .C C C = 720 cch
0.25
Scch chn 4 vin bi khng c3 mu : 1365-720 = 645 cch 0.25
Cu V(1)
Xc sut cn tm : P =645 43
1365 91=
0.25
7/21/2019 [DeTHiThuDH.net]-De Thi Thu THPT Quoc Gia Lan 1 Truong Ly Tu Trong Khanh Hoa
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Trang 4
JI
N
MG
O
C
AD
B
S
Gi O l giao im ca AC v BDS.ABCD l hnh chp tgic u nn SO (ABCD)Gi I, J ln lt l trung im ca AB v CD , xc nh c gc gia mt bn
(SCD) v mt y (ABCD) l 060SJI = .
0.25
Nhn xt SIJ u ; SO =3
2
a; VS.ABCD =
31 3.
3 6ABCDa
SO S = (vtt) 0.25
Trong (SAC) , AG ct SC ti M , M l trung im ca SCC/minh c MN// AB v N l trung im ca SD
.
1 1
2 4
SABMSABM S ABCD
SABC
V SMV V
V SC
= = =
.
1 1
4 8SAMN
SAMN S ABCD
SACD
V SM SN V V
V SC SD= = =
0.25
Cu VI(1)
3
. . . .
3 3
8 16S ABMN S ABM S AMN S ABCDa
V V V V = + = = (vtt)0.25
Gii hphng trnh :3 2 3
3 2
6 13 10 (1)
2 5 3 3 10 6 (2)
x x x y y
x y x y x x y
+ = + +
+ + = +
(1)
3 3(1) ( 2) ( 2)x x y y + = + Xt hm sf(t) = t3+t , t R c f (t) = 3t2+1>0, t R f(t) ng bin trn R v (1) 2x y = (3)
0.25
Thay (3) vo (2): 3 2 53 3 5 2 3 10 26 (4); 12
x x x x x x+ = + 0.25
+ Chng minh g(x) = 3 3 5 2x x+ ng bin trn on5
1;2
+ Chng minh h(x) = 3 23 10 26x x x + nghch bin trn on5
1;2
g(2) = h(2) = 2 x=2 l nghim duy nht ca pt (4)
0.25
Cu VII(1)
p s ( ) ( ); 2;0x y = 0.25
Cho 0,, zyx v 3=++ zyx .Tm gi trnhnht ca biu thc:
xzzyyxP ++++++++= )1ln(241
)1ln(241
)1ln(241
Cu VIII(1)
Vi cba ,, >0,p dng bt ng thc Csi ta c :1 1 1 1 1 1 9
( ) 9a b ca b c a b c a b c
+ + + + + +
+ + (1)
Du = xy ra cba ==
p dng (1) ta czzyyxx
P++++++
)1ln(2)1ln(2)1ln(212
9
0.25
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Trang 5
Xt [ ]3;0,)1ln(2)( += ttttf
t
t
ttf
+
=
+=
1
11
1
2)(' ; 10)(' == ttf
32ln4)3(,14ln)1(,0)0( === fff 14ln)(32ln4 tf
0.25
12ln 2 9 ( ) ( ) ( ) 3ln 4 3
12ln 2 3 ( ) ( ) ( ) 12 9 3ln 4
f x f y f z
f x f y f z
+ +
+ + + + +
9 9 3
12 ( ) ( ) ( ) 9 3ln 4 3 ln 4P
f x f y f z =
+ + + + +
Vy 3 13 ln 4
MinP x y z= = = =+
0.25
Mi cch gii khc ng ca hs u cho im tng ng vi mi phn ca cu