Đề thi KS chất lượng đầu năm học 2017 môn Toán Lớp 12

Di, KIEM TRA CI{AT LIIQNG DAUNAM
NAM Hgc 201G2017
M0n thi: Toin 12
Thiri gian lim biri: 180 phit, khdng k6 thiri gian ph{t dii

SO GT} $ DT BAC NINH

TRI'ONG THPT HAN TIilTY$N

Ciu I (t,0 -li6m).

l.

Cho n ld sli tu nhi6n th6 a menC| = 45. Tinh gi6

2.

Cho

/(x)

= sin2x+cosx

bi6u thric

1 - 24

.fi* f'(r)

Ciu II (1,0 ili6m). Cho mm st5 71x; = mxt - 3x'
Ciu III. (r,0 ili6m). Cho him ,6 y =:l+

r ^ i
. ,:,
ne so goc Dang -

t{

.

+ nu +

l.

Tim m d6

/' (r) > 0, Vx e R.

Vi€t phuong trinh ti6p ruy6n voi

AO

tH Ui.it ti6p tuyiin c6

i

Ciiu IV (1,0 ili6m). Tinh gioi

tt*
hry*#
' x+2.
yt

+5x_14

Ciu V (1,0 iti6m). Trong m4t ph'ing voi hQ tqa d0 Oxy,

cho hai di6m A(1;2),

Bt3;l). Vitit

phuong trinh

duong thing iti qua hai
li

rE ysi O

g6c tEa itQ.

Ciu YI (1,0 ili6rn);

luy€n vi6n cua m6i dQi cAn trintr

tro. ng

tii

m6t danh s,ich slip thu t.u 5 cAu thu rong sa t

cAu thri

cic ciu thri tl6 c6 hai ciu thu Tin vi C6ng. Tinh xric suit

dC d6 luAn

luu 1l mdt. Trong

thiTin vi

C6ng c6 m{t trong s6 5 ciu thri di ludn luu.

sd

t

i-

t

dA cAu

.,

Ctu VII (1,0 di6m). Trong lfi6ng gian cho hinh ldng tru ABCA'B'C' c6 d6y ld tam gi6c vu6ng d C, AC

:

4 AB = 2a Hinh

vi

A' tdn m4t phing (ABC) H trung
ducrng theng

A'C

mdt phing (ABC) bin€ 600. Tinh di€.n tich tam gi6c ABC, chiAu cao cua kh6i t4r vA cosin g6c

gita

hai ttudng

chii5u cua

thingA'B

Cau 14II (1,0

ifi6d.

vn AC.

Trong m{t phing voi hQ tga tlQ Ory, cho tri gi6c ABCD nQi ti6p trong rtudng trdn,

hai ttudng chdo vu6ng g6c voi nhau vd

cit

Ciu IV (1,0 iti6n). Giai bdtphuong tdnh

Cliu V (1,0 tliSm). Cho x,y,z lAba

l.

Tim

st5

nhau tai

E(l;-l). Hinh chiiiu cua E l6n duong thing CD h

Jir-r-x'

-Jzx+5+t


duong thda miin x2 +y2 +22 +2xy =3(x + y+ z).

gind kin nhat cua t=x+y+z

2. nm giefrinh6 nhit cua biAuthric I

=

"

+y

+,

+

#.#

...H&..
Ha vdten thi

sinh

...............56

b6o danh.


'

50GD) i)l:,..;TRTTO\'G

.-.

:.-..

.. ...1

ttlU\trU.\\(i,l

,

Ei

TIPT F!\.\ TiJL'i.T

hJE.U TRA

CIi.\T LL'I'J\L;

|

D

\L'.\ i.\I

NAII rIQC 2016-?0r:

ilIo|i: ToiN 1:
Ciu

I

NQi dung-ddp

eff

l.+) DK: n> 2;n

.

khi d6

C"z

in

Di€m

02s

=90€r?=10

02s

-24 =361872O
2.+) f (x)=2cos2r-sinx

02s

+)f {r):z

03s

+) P,,

tr

+)

f

(r) = 3mxz -

+)m=0. tac6

6x +

m> o,vx e R

f (x)=-6x;

0,2s

02s

"f'(t)>-0 <=x<0(loai)

-r)m+u.;
0'5

r1r)
EI

+)

>

o,

vr

e .n
1

f (r) = ------i(x
+

=

o o. . <.6

"

a2s

2)'

+; M (ro ; yo ( xo
)

* -2 ) h titip di€m cria tiiSp tuy6n.

0,25it

=-1'+Yo=4
lxo =-l=yo =-19

f'(x^\=-7 <>l

+)ro =

+) ro

-f

;

ro

plg66g trinh tiiip

nry6n :

!

= - 7x - 3

0ts

=-f ;pttty= -7x-31

IV

0,25

(J, *z -zl(J-*z *z\
\
,f\'
/

!\I-l;-

'

- {l : : * {^ ={:r:,=, * {_si.'

'+2 (x2 + 5.r

- l4)lJ.r

+2+

0,25

2)

t:?
= linr ---- L-----'" (x-2)(x +1)lJx+z+z)'-:(x+7)(J.r+2
--

*1 = 1;*

+z)

I

0'5

0,25

JO

v

7:0
+)c1i M (4n -7;n) e AB gld'z = (am -7\t + *, = 5 e 17mz - 56m + 44 = 0
=
+) phuong trinh tludng thing qua 2 ditim A, B lex

-4y+

0,5

0'5


1i

,t

| x=tr+k2tr
icosx=-1
I --fcos-r=)+)i
1ei
.r
Lx=!-:+k2n
2)+) Sd phan tu kh6ng gian m5u lOl

:

0rs

,e,1

+)Ggi A ld bi6n cii " Trong s5 5 ciu thri chon ra dd al6 ludn luu c6 m{t hai ciu thri
TAn

vi C6ng" =

lQ, | = Cr'.5

lol

1

0,25

.

.)

Yiv P(A\=1'-!='

lol

\rII

1r

0as.

n'.11
+lBC=aJ3=S".-.=*
"'*-2

+)@,(.4BO) =@c.ca)=Ecu

=ao" .Chidu cao A'H = HC.tan60o

le's.ACl

+)-

cos(e'.B.;c)
\ . I AB.AC'

'\t2

{mg

li

+) Chung minh M

+

0,25

cei r(a;-3)

tnrng diAm AB

lB; MA: ME *

e

0,25

- U(1t-l\
\2 )

02s
0

=
=2 * + olo
f"-:'l'
\ 2,1 4
la=5

0,25

l(s;-3),.8(0;-3)
0'2s

+) phuong tinh CD: -3x+4y-3:0
Pt BD: 2x-Y-3=0

D --CD n BD

>

D{3;3)

ptAC: x+2y+1:0; C = AC r-tCD

= C(-l;0)

vay A(5;3), B(0;-3)- C(-l r0). D(3:3) vn

w

-?

=L

gita hai tluong th5ng.

g6c

+) Phuong trinh Ei:4x+3y-l=0

+)

025

.l
coslAB;ACI=:-

C2: hs

vrn

ali

0,25

A'B =2a

+\ A'B.AC =T E A + AAI.AC = IIB.AC = AH.AC
YQy

=

+) DK

-5

-
ti \zl,-, /I


.!-=:--

+) (*) c+ / s a

=

rr';6-'3

I.,"1

-1

1..,12r+5

e.,i-xr -x+12
€.( [

€r f>--

'>l

1+'u64

l2x'-r-11>0

+; K6t

hqrp

ttiiiu kiQn L

6oo.

lJ it2 =,
"

=3

l.) +)3(x+y+21=e+y)] *r' u('*y-*'\' =x+y+z<6.
z
khi x

+\T )

:

1

y

;y = 2;z = 3. Vdy x + y + z lon nhAt bing 6

80
- J'+'+.[yi-''''-

-r-

>x+

0,25

D6u bdng xay ra

k*i x :l' y = 2' z = 3.
160

2.J;i+2.Jy+z

r6n
320
> x+ y+z+L
y+z+;-----fr
'
4+x+z
x+y+z+10
22 +++y+t

+)Ddtt=x +y+2,0
r

>t

*
.,

::|

.Vay gie

fi

.

= {r + 1 0) +
,

i

+

05
+

fi6

' nhat
'
nhd
ctia T b6ng 26 khi

o)ffi

ro

> z11r +

r

x:

\t y : 2'

z

-

:

3.

+

;ft

_10 = 26