THPT chuyên KHTN lần 3 năm 2017 + lời giải chi tiết + môn toán

Trang 1

-

Câu 1: 0

90

A 3 a 3  B. 3 a 2  C 3 a 4  D 3 a 4 Câu 2: 2 2 1 4 ln x 1 dx a ln 2 b ln 2 x     g 4ab

A 3 B 5 C 7 D 9 Câu 3: yx2 y x

A 1 2 ( d ) B 1 3 ( d ) C 1 4( d ) D 1 6 ( d ) Câu 4: mx 1 x m  

A m  1;1 B m 1 C m 1 D

Câu 5:

3

dm

d (

)

( d )

(

) d

A a 24, b 21 B a3, b8 C a3 2, b4 2 D a4, b6 Câu 6: 3

yx 1 2

yx x

A 0 B 1 C 2 D 3 Câu 7: ABa; AD2a AA '3a

d

Trang 2

A a 3

a 14

a 6

a 3

4

Câu 8: ( )

d

A

2

5 a

3



2

5 a 6



2

a 3



2

5 a 12



Câu 9:

A yx4 x21 B yx4x21

C y  x4 x21 D y  x4 x21

Câu 10:

SAa 3

A

3

a

3

a

3

a

3

a

6

Câu 11: 3x43x2 81

Câu 12: m ln 1 x  ln xm x 0;1

A m0; B m 1;e C m  ;0 D m   ; 1

Câu 13:

2

x y

x 1





Câu 14: 3 1

2

log log x 1



A  0;1 B 1;1

8

 

 

  C  1;8 D 1;3

8

 

 

 

Câu 15: y x

x 1





A  0;1

B H R \ 1  

C   ;1 1; 

D ;1 1;

Trang 3

Câu 16: z 4 3i  3 z 0

z 0

A 3 B 4 C 5 D 8 Câu 17:     x

F x  axb e   x

y 2x 3 e ab

A 2 B 3 C 4 D 5 Câu 18: ( )

d :1 x 2 y z 1 1 1     2

x y 1 z 2 d : 2 1 1       A  P : 2x 2z 1 0   B  P : 2y 2z 1 0   C  P : 2x2y 1 0  D  P : 2y 2z 1 0   Câu 19:

      A 1; 2; 1 ;C 3; 4;1 , B' 2; 1;3   D ' 0;3;5   D x; y; z  

x2y 3z

A 1 B 0 C 2 D 3 Câu 20:  P : 2x2y z 3  0

  x 1 y 3 z d : 1 2 2     (d) ( ) (d)

MA 2 ( )

A 4 9 B 8 3 C 8 9 D 2 9 Câu 21: SA.en.i d

d d d d d

d d

A B

C D

Câu 22: 3 2

Ix x 1dx

A 2

1

1

t t 1dt

1

1

t t 1dt

2  C 3 

2

0 t 1 tdt

0 x 1 x dx

Câu 23: Cho alog 202 log 5 theo a 20

Trang 4

A 5a

a 1 a



a



a 2





Câu 24: yx33x2 d

sau: 3 2 y x 3x

A 0 B.1 C 2 D 3 Câu 25:

2 1 x 2x y x 1    

M m

A -2 B -1 C 1 D 2 Câu 26: 3 2x 1 3x 1 x22x

A 0; B  0; 2 C 2; D 2;   0 Câu 27: ( ) ( )

0

60 BABCa

d

A 3 a 3 4 B 3 a 3 6 C 3 a 3 24 D 3 a 3 8 Câu 28: x1

  3 2 2 1 x mx m m 1 x 3     A m   2; 1 B m 2 C m 1 D

Câu 29: z a bi

z

A z2 a2b22abi B z2 a2b2 C z22az a 2b2 0 D z22az a 2b2 0 Câu 30: yax3bx2cx d 1;18 3; 16 

a  b c d

Trang 5

Câu 31: yx44x23

x   2 0 2 

 

f ' x - 0 + 0 - 0 +

 

f x  3 

-1 1

4 2

x 4x 31 m

A 1 m 3 B m3 C m0 D m   1;3  0

Câu 32:    2

f x ln 4xx

A f ' 3  1,5 B f ' 2 0 C f ' 5 1, 2 D f '   1 1, 2

Câu 33: ( ) A 1; 2;1 ;  

B 3; 2;3  P : x  y 3 0 ( )

Câu 34: y2sin 2x

A 2sin x 2 B 2cos x2 C  1 cos 2x D  1 2cos x sin x

Câu 35: Trong A 1; 1;1 ; B 2;1; 2 , C 0;0;1       

H x; y; z  x y z d

Câu 36:

2x2y z 3  0

Câu 37: z 1 1

z

  z2017 20171

z



Trang 6

Câu 38: d

A 1; 2;1 , B 0;0; 2 ;C 1;0;1 ; D 2;1; 1  d

A 1

2

4

8

3

Câu 39: Cho xlog 5; y6 log 3; z2 log 10; t4 log 57

A z  x t y B z  y t x C y  z x t D z  y x t

Câu 40: d n

1

n ln n ln xdx

2017

A 2017 B 2018 C 4034 D 4036

Câu 41: ( ) ( )

( ) 3

a

A 3

3a

Câu 42: 3iz 3 4i  4z 3z4

Câu 43: a, b, c0;a  1; 0

A loga bc log b log ca  a B loga b log b log ca a

C loga b log ba D log b.log aa c log bc

Câu 44: A 3;0;0 , B 0; 2;0 ;C 0;0;6     

D 1;1;1     d

A M 1; 2;1 B 5; 7;3  C 3; 4;3  D 7;13;5 

Câu 45: d 3 2i d  1 6i d

A 1 2i B 2 4i

C 2 4i D 1 2i

Câu 46:

d

Trang 7

d d

d d

d d

d (

10km / h  )

d ;d ;d 1 2 3

A d1d2 d3 B d2 d3 d1 C d3d1d2 D d1d3 d2 Câu 47:

CACBa;SAa 3 ; SBa 5 SC a 2

A a 11 6 B a 11 2 C a 11 3 D a 11 4 Câu 48:

A  10 1 i 32 B  10 1 i  32 C  10 1 i 32i D  10 1 i  32i Câu 49: a, b0

2 1 3 3 6 6 a b b a a b  

A P ab B 3 P ab C 6 P ab D Pab Câu 50: SAa;SB2a;SC3a

A 6a3 B 2a3 C a3 D 3a3 p

1-A 2-D 3-D 4-A 5-D 6-C 7-B 8-A 9-C 10-C 11-A 12-A 13-C 14-B 15-D 16-D 17-B 18-B 19-B 20-C 21-A 22-A 23-C 24-D 25-D 26-D 27-D 28-D 29-C 30-B 31-D 32-B 33-D 34-D 35-A 36-A 37-C 38-D 39-D 40-B 41-D 42-B 43-C 44-B 45-D 46-D 47-B 48-C 49-B 50-C

L I GIẢI CHI TIẾT

Trang 8

Câu 1: p A

p p d

AC2r2a

AC2a

( ) a

    

Câu 2: p D

p p

4 ln x 1 4 ln x 1



1

4 ln x 1 4 ln x 1



1

2ln x ln 2 2ln 2 ln 2

Suy ra a2; b 1. Suy ra 4a b 9

Câu 3: p D

p p d d

2

x x

x1 x0

d 1 1 

1

0

Câu 4: p A

p p

0

xlim yx

   xx0

x m 0 xm

xm l m.m 1 0 nên m 1 m 1

Câu 5: p D

p p d Vab.3 72 Suy ra ab24

+ S3a.3 3b.2 ab  9a 6b 24 

Trang 9

9a6b

9a6b2 9a.6b 2 54.ab729a6b ab24 nên a4; b6

Câu 6: p C

p p 3 2

x  1 x x

3 2 x x   x 1 0   2  1 2 x 1 x 1 0 x 0; x 1        

Câu 7: p B p p

d

1AC ' 2 2 2 2 2 2 AC' AC AA '  AC CB AA '  2  2 a 2a 3a a 14     Suy ra OC a 14 2  Câu 8: p A p p

0

SDC90 d ( ) (

)

ISIBIC

d ( )

( )

( ) CD / /IM

song song v

Trang 10

ra IM DL 1CD 1 a 3 a 3

2 2 5

12

2

khoicau



Câu 9: p C

-

y '0

 4 2 

     

Câu 10: p C

day

V SA.s a 3 .a.a.sin 60 a

Câu 11: p A

4 2

3  81 3 x 3x   4 0 x    4 x 2

Câu 12: p A

p p      ln x

m ln 1 x 1 ln x m

ln 1 x 1

  1 x 0

 ln x 0 0<x<1

ln 1 x 1 

 

 ln x

y

ln 1 x 1



  d d

- - ln x.ln e

1 x

-

Câu 13: p C

yb

n ngang

Trang 11

2

2

1

x 1

1 x

2

1

x 1

1 x

Câu 14: p B

p p log ba log c ba  ckhi a1

0 1

2

1

2

 

 

3

1 log log x 1 log 3 log x 3 log

2

3

Câu 15: p D

1

x 1



Câu 16: p D

z x yi; z 4 3i  x 4  y 3 i 

z 4 3i   y 4  y 3 i   2 2

I 4; 3 ; R   3

y 3sin t 4

y 3cos t 3



x y 3sin t 4 3cos t 3

9sin t 9cos t 24sin t 18cos t 25

24sin t 18cos t 24 18 sin t cos t 30

Câu 17: p B

p p ab

  x   x

y 2x 3 e  2x 3 e dx x x

u 2x 3 du 2dx

dv e dx v e



2x 3 e dx  2x 3 e  e 2dx 2x 3 e 2e  2x 1 e

a b 3

Câu 18: p B

Trang 12

p p ( ) d

d 1 d 2

d 1 u1   1;1;1 d 2

2

u  2; 1; 1 

( ) ( )

uu , u  0; 3;3 3 0; 1;1

Trên d 1 M 2;0;0 ;   d 2 N 0;1; 2  

 P : 2y 2z a  0

( ) ( )

a 2.1 2.2 a

Câu 19: p B

p p

1

MD B' D '

2

M 2; 1;0  

B' D ' nên N 1;1;1  

D x; y; z  

MD B' D ' 2; 4; 2 1; 2;1

Suy S 1;1;1 Suy ra   x2y 3z 0

Câu 20: p C

p p

A a 1; 2a 3; 2a   

  P : 2 a 1  2 2a 3  2a 3 0 Suy ra a 1 A 5; 5 1;



Trang 13

M m 1; 2m 3; 2m   ;

             

Suy ra m 11

12

 m 5

12





M 23; 7 11;

12 6 6



8

d M, P

9



( ) d 8

9



Câu 21: p A

d 3 1,03.10 3 2 

S 94970397.e 98



 

Câu 22: p A

2 3 2 1 I x x 1dx 2 dt x t xdx 2    x 1 t1; x2 t4 4 1 1 I t t 1dt 2    Câu 23: p C p p d

2 2 2 20 2 2 1 log 20 log log 5 1 1 4 a 2 log 5 log 20 log 20 a 4 a a                Câu 24: p D

3 2 y x 3x Câu 25: p D p p

1 x 0

2

  1 x 0 x0, max y 1

Trang 14

1 x 2x 1 x 2.1

  1 x 0 x1, min y 1

max y min y 2

Câu 26: p D

x0

x 3 2

x1

Câu 27: p D p p

( ) ( )

SBA

0 60 0

SAAB.tan 60  3a 3

ABC 1 1 1 3 V SA.S a 3 a.a a 3  3 2 6    SAMN SABC V SM SN 1 1 1 V  SB SC 2 2 4 Suy ra VAMNBC 3VSABC 3 3a3 3a3 4 4 6 8    Câu 28: p D p p

2  2  y 'x 2mx m  m 1 x1 2

2m m   m 1 0

Câu 29: p C p p

A z a bi z  a bi ( )

2 2 B z  a b ( )

C z a bi; z a bi ( )

Trang 15

Câu 30: p B

p p

d

2

y '2ax 2bx c

x 1 x3 y '0 3a2b c 0

27a6b c 0

18 a b c d

16 27a 9b 3c d

    

a 17; b 51;c 153;d 203;

a b c d 1

    

Câu 31: p D

- y x44x23 d

m   1;3  0

y d

y

Câu 32: p B

2

4xx    0 0 x 4

  2

4 2x

y ' ; f ' 2 0

4x x



Câu 33: p D

p p ( ) I a; b;c  

( ) I a, b, c Suy ra   a      b 3 0 a b 3 I b 3; b;c  

IA IB R  b 2  b 2  c 1 b  b 2  c 3

c 1 2b 

  2  2 2

R  b 2  b 2  2b 4b    8 8 R 2 2

Trang 16

min R2 2 khi b0

Câu 34: p D

2

1 cos 2x  2cos x

2sin x 2 2cos x

Câu 35: p A

p p d

AB 1; 2; 3 ; BC    2; 1;3 ; AC 1;1;0

AB; BC 3;3;3 n 1;1;1 ABC : x y z 1 0

AH x 1; y 1; z 1 ; BH x 2; y 1; z 2 ;CH x; y; z 1      

5 4 8

BH.AC 0

9 9 9

x y z 1 0



      



Câu 36: p A

3

Câu 37: p C

p p d

1 2 1 3

         ( )

Suy ra 20171 1 3i

z  2 2

Câu 38: p D

p p d d

1

V AB AC, AD

AB1; 2; 3 ; AC   1; 2;0 ; AD  3; 1; 2  

Trang 17

AC, AD 4; 4; 4 u AB.u 16

Câu 39: p D

zy (d )

yx (d ) x t

Câu 40: p B

p p

: n

1

I ln xdx

ln xu Suy ra 1dx du;dx dv v x

 

n n

x

I x ln x dx n ln n n 1

x

n 1

n 1 2017  n2018 d

Câu 41: p D

33

1

1

3

  3

Vhs3a

Câu 42: p B

4 3i



Câu 43: p C

p p d

c: a a

1 log b log b

Câu 44: p B

x y z 1

3  2 6

D 1;1;1  ( ) ( )  AHAD

BIBD;CJCD

  ( )

Trang 18

 ( )

x 1 y 1 z 1

    

M 5;7;3  

Câu 45: p D

d d abi

a 3 1 1; b 6 2 2

    ( )

Câu 46: p D

p p d

d

2

v v0 4   2

t h a 900km / h

2

0

   ; Sd1 6km

d2 8, 75km;d3 20km

3

Câu 47: p B

- d

-

- SJ SI 5 1,12

2

   Lo

- r 11a

2



JL 2a

- IJ 6a

2



- IL 2a

2



Trang 19

- IL 1AB 2a

 

Câu 48: p C

 10

1 i 32i