De thi Dap an HK2 khoi 12 BTRE nam 2012

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(1)<div class='page_container' data-page=1>

so

GD&DT BEN TRE

BE

KIEM TRA HOC KY II LOP 12
NAM HOC 2011-2012

Mdn Toan Giao due trung hoc ph6 thong

( Thili gian film hili 150 philt, khong ki thiligian giao ttJ)
I. pHAN BAT BU<)C (7,0 c1iim)

Cau1 (2,5 c1dm) .

, 2

f

J =2

fx

2

+

Fx

+

dx .
a)Tinh cac tich phan sau: I

=

sinx.e'?" .dx va

o

.

.1.

x

b) Tinh dien tieh hinh phang gioi han boi d6 thi (C) cua ham s5 y =x3 -x va true Ox.

Cau 2 (2,0c1dm)

a) Giai plnrong trinh Z4 - Z2 - 6

=

°

tren t~p s6 phirc.

b) Trang matphang toa dQ Oxy cho cac diem A, B, C IfuI hrot la cac di€m bieu di€n cac s5phirc
z\

=

2 +3i, Z2

=

-2 +i va Z3

=

-3 +3i .Chirng minh tam giac ABC vuong tai B.

Call 3 (2,5 c1dm)

Trang khong gian voi h~toa dQ Oxyz cho tam giac ABC voi A( -1;2;1), B(1;-2; 3) va C(1; 2; ~1) .
a) Vi€tphuong trinh tfmg quat cua mat phang (a) di qua ba diem A, B, C. .
b) Vi€tphirong trinh tham s5 cua dirong thang I:i di qua trong tam G cua tam giac ABC va vuong

g6e voi m~t phang (a) .. .

c) Vi€t phirong trinh m~t cftu (S) e6 dirong kinh AB. '

II.pHAN

TV

CHON (3,0 c1iim)

Thi.sinh chon mot trong hai phdn (phdn A hoac phdn B)

1 . . •

1. Phan A theo chuong trinh chuan:
Ciiu 4A (1,5 c1iim)

a) Tinh tieh pharr I .,

f

(2x + 1).lnx.dx .

b) T'im mocun~ eua so p ire z, :.. h'

= --.

+

2i+ +1 2·1.

. 1-1

Ciiu 5A (1,5 c1iim) Trang khong gian voi h~toa dQ Oxyz eho m~t phang (a) va dirong thang !::,.

Ian trotl I co p uong' h tninh

lr

a: x +2y -2Z+

1 °

'

x-I y+2 z-2

=T va -

=

--

= -.

. 1 1 -2

a) Chirng minh rang duong thing !::,.e~t mat phang (a). Tim

toa

dQ giao diem.

b)Tim cac di€m M thuoc dirong thang z; sac eho khoang each ill M d€n m~t phing(a) bang

J2

.

2.Ph§n

B

theo chuong trinh nang cao:

Cau 4B (1,5 c1dm)

, x

a) Cho hinhphang

A

gioi han boi cac duong y=xe2, y=0, x=0, x =1. Tinh th€ tich khoi tron
xoay tao thanh khi quay hinh A quanh true hoanh.

b)Vi€t s5 phirc Z

=

(1- iJ"j)(1 +i) duoi dang IUQTIggiac.

Call 5B (1,5 c1iim) Trong khong gian voi

M

toa de>Oxyz cho mat phang (a) va dirong thing !::,.

Ian uotll' co p ironh g tninh la:' x+ 2y- 2z+ 1=

°

va,x-.1-=--=-y+2 z":2

. 1 1 -2

a)Chung minh r~ng dirong thing !::,.e~t m~t phang (a) .Tim toa dQ giao di€m.

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---II€t---HUONG

DAN CHAM

CUA DE KIEM TRA HQC KY II

N

A

M

HQC 2011 -2012

.

MON

TOA.N - KIIOI 12 -

Gia

'

o

due

trung

hoc

phB thong

(Huang din cham gom 05 trang)
Call

Call 1
2.5 d

Dap

a

n

a) Tinh cac tich phan:
tr

1= fSinx.ecosx.dx D~t t=cosx ~ dt =-sinxdx
a

X=- ~t=O

Diem

0,25

0,5

0,5
tr

j a I

1= fSinx.ecosx.dx = -

f

et

.dt =et ~ e-1

a 1

2x2+Fx+1 2 1 1

f

dx=

f(x+-+-).dx

1 X 1 Fx X

2 2

= (~+2Fx +

mlxl)

2 1 0,5

=

2J2

-

.

!

.

+

ln2
2

0,25

.b) Tinh dien tich hinh phang gioi han boo

d6

thi (C) cua ham sf>y =x3-X vi true
Ox.

.Phuong trinh hoanh d¢ giao difm CM (C) va true Ox. lilx' -X ~ 0

¢'

> [ :

: ~

1 0,25

a 1

G9i S la dien tich cAntim ta c6: S=

f

(x3._ x).dx

+

f

(x' - x).dx

-1 a

0,25

0,5

(

X4 X2

J

a (X4 X2

J

1 .

-

---

+

---

=- (dvdt)

4 2 4 2 ·2

·1 a

Cau2

·,,2.0d I,,· . 'c.

L---__ --" ~ .~______________________________________________ _ _
.. .a) Giai phirong trinh tren t~p

so

phirc:

Z4 -"'Z2 -6 =O.

.

..

...

.

..

[t

=-2
D~t ~·t=Z2 phuong trinh c6 dang t2 - t - 6=0 T-r'

t=3

2

[z

=

rJ

'

2

t=-2 ~ z =-2

¢:>

z

=

-i

.

J

2

t== 3

=>

Z2

=

¢:>

Z

=

±J3

b) ZI =2+3i, Z2 =-2+ivi Z3 =-3+3i.

=

>

A(2;3), B(-2;1), C(-3;3) .0,5

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,---,--

- - - -

-- - -- -- - - -

- -

-- - - -- ---

-

- - -

-

- - - -

- - -

-

- -

-

-- -- - -- -- --

-

- -

-

----

-

- - -

- -- - ---

-

--- -

-

--- --

--AB=,j42 +22 =2J5; BC=,j12+22 =J5; AC=.J52 +02 =5

AB2+ BC2

=

AC2.V~y tam giac ABC vuorig tai B. 0,5

Cau3

2.5<1

Cau4A

-15<1

,

A(-l;2;l),B(1;-2;3)

va

C(1;2;-l).

a)Vi€t phirong trinh t6ng quat cua m~t phang {a).

,AB(~;-4;2); BC(0;4;-4) ~ [ AB,BC ]

=

(8;8;8)

,

[J

'O~

n(l;l;l) Ta co n, AB,BC cling phirong

---.--- ---

---M~t phang (a) nhan n lam VTPT

va

di qua cii€m A.

V~y (a): x+y+z-2=0. 0,25

b) Viet phuong trinh tham

so

cua dirong thang ~ di qua trong HimG cua tam giac

ABC va vuong goc voi mat phang (a).

, 0,25

G(l;%;l) la trong tam cua tam giac ABC.

--~

-di-~~~-

G-

~i-~6-~~

-~6-~-~&i

-~~~-

~h~~~

-

(~)-,-

-;;

-;

-~~

-~

-

ii~

-VTCP-

---

---, ---

-1

x=-+t

3
2

,V~y PTIS cua duong thang ~

y

= -:-

+

t

, 3

z

=

1+ t

0,5

c) Viet phirong trinh mat cau (S) co duong kinh AB.

1(0;0;2) la trung di€m cua AB. 0,25

--

~

X~t

--

c~

i

-

(sj

---

c6

-

duln{g---k

,

iiih

-

AB

-

--

llh~n

--

i

-

--

i~m

-

t~~

-

v~

--

-c

6 -

-

b~n

--

i

Ci

r

i

li

-

~-

-

---

-

-R

=

216

=

16

.

0,5

'22, .

--- -_._---

----V~y' (S): X2+y2 +(z-2/ =6 0,25

2 , '

,a) T~ tich pharr 1= f(2x + l).lnx.dx .

, - 1

0,25

,{" 1

, u =lnx ~ du = - dx '

Bat x '

dv=(2x + 1)dx ~ v=X2+X

---2---'. ---2---.---_.-._--- --- ..

=

f(2X + l).lnx.dx

=

[(x2 + x)lnx

JI:

-J(x + l}.dx

1 1

</div>
(4)<div class='page_container' data-page=4>

, 0,25

b) T' 'd . :.. ht 3

+

2i 1 2·

, im mo un cua so p ire z= -'-.

+ +

1-1

3 +2i t 2· (3 +2i)(1 +i) 1 .

Z=--+

+

1= + +1 0,25

l-i 2

--- ---

-1+5i 1 2. 3 9.

=--+ + 1=-+-1

2 2 2 0,25

VAay :Mod0 uun cuan cf Zl'a

JP!81

+ -

'

= --

3M

. 4 4 2

Cau'5A
1,5d

,,'

Cau4B
1,5d

Trong khong gian voi h~ toa d<)Oxyzcho mat phang (a) va duong thllng b. l~n
1trot co pionhtroiuang triri'001'a: x+2y -2Z+1

=

0 va''~x-I

= --

y+2

=

--.

z-2

. '1 1 -2

a) C~(mg m~nh{~:~ :~(mg thang b.c~t m~t phang (a) .

~TTS cua b. y =-2+t
Z= 2-2t

Xet phirong trinh: ( 1 + t + 2(- 2 + t) - 2

(2

-

~t) + 1 = 0 <=>7t -6= 0 <=>t =

%

0,25
13

-7

-8

~ Y

=-7 '

Z=~ 0,25

~

~;;-

~~~~

-

~~

-

~

-

~~

;;:;;-p~h~-~

-

~;~;

-

~

l

¥-;

-

+n

----

-

--

-

---

-

---

-

---

~:;~

---b) Tim diem M thuoc dirong thang. b. sac chokhoang each illM den mat

phang(a) bang

.

fi

.

,MEb.~M(1+t;-2+t;2-2t)

0,25

~ d(M;(a))

=

.

fi

<=>17t;61 ~

J2

<=>17t- 61=

3J2

6±3J2

<=>t=---7

0,25

V~y:

M(~3+3J2.

-8+3

.

fi.

2-6.fiJ.

, 7' 7 ' 7 '

, ,

M(13-3

.

fi

.

-8-3

.

fi

.

2+6fiJ

7 " 7 ' 7 0,25

</div>
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.---,... . .

'Call 5B

1,5.d,

0~25

,''''

L...-__ -' •••••••••••••••••••••••••••••••••••••••••••••• '•••••••••••••••••••••••••••••••••••••••••••••• _•••••••.•••••••••••••.••••

x

a) Chohinh phang A gioi han boi cac dirong y

=

xe2,

y=

0, x

=

0, x

=

1. Tinh
th€ tich kh6i trim xoay tao thanh khi quay hinh A quanh true hoanh.

GQi V la th€ tich dn tim ta co V

=

n

f

ex .dx

{

=

X2 =>du

=

2xdx

Bat

. dv=edx => v=eX

1 1

V =n

f

x2ex .dx

=

n(x2eX

I~

-

f

x.e"

.dx)

o' 0

,0,25

=

n(e -2J)

----------------------------------------------------------------------------------------

---,1 {u

=

X =>du

=

Tinh J

=

I='

.dx Bat

. . dv=eXdx => v=eX

o .

1 1 1

J

=

I='

.dx

=

xet -

fex .dx

=

,0 0

0,25

V=7r(e-2) (dvdt) 0,25

V~y:

b) Vi~t s6 phirc z

=

(1- iF3 )(1

+

i) duoi dang IUQ1lg giac,

(1-

iF3J

2[COS( -;)

+

iSin( - ;)

1 .

Trang khong gian voi

M

toa d(>Oxyz cho mat phang (a) va duong thang !::. Ifin
Itrot co p irong tn

x

oh inh lsa: x+ 2y- 2z.+1

=

° '

.

va -1-x-I

=

-1-y+2

=--=2

z-2

a) Chirng minh rangdtrong thang t3.c~t mat phang (a) .

{

X =l+t

PTTS cua t3.

y

=-2

+

t 0,25

z=2-2t

Xet

,

Phuang trinh: ( 1

+

2(- 2

+

t) - 2 (2 - 2t)

.

+

=

°

¢:> 7t -

6 =

°

¢:> t

= ~

7

------------------------------------------------------------------------------

---13

X=-7

-8

0,25

=>,

y=-7

</div>
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,---, -

- -

- - -

- -

---

-

--- - --.---

- -

-

- -

-

- - -

-

- -

- - - -

_.-

- - -

-

- -

-- ----

-

- - -

-

- -

-

- - -

- --- - - -

- -

- -- -- -- --.-- - -- -- - --

-V

ay:A f)i'rong t an

h

'

"

g A; -

h

'

" (

)

- A (13

8 2)

ucat mat pang

a

tar .'

7;-7;

7

0;25

b) Tim diem M thuoc dirong thang 6. sac cho khoangcach nr M den mat

phang (a) bang

..

fi .

ME 6.

=>

M(l

+t

;-

2+t;2-2t)

0,25

-

~

-

~

(~

~~;-;~-Ji-~

;

-li~+-t

-

~4

+

2t~4

+

4t

+-11-~

-h

---

-

--

-

---

-

---

-

--- ---

---

-

---. - 3 .

~

1

7t -

61 =

3

..

fi

0

,

25

6±3

..

fi

~t=---7

-_.------------------------_.-------.------------------------------------------- ---

-vsv.

M(13

+

3

..

fi .

-8

+

3

..

fi

.2 - 6

..

fiJ.

M(i3

-3

..

fi .

-8

-

3

..f

i

.

2+ 6

..

fi

J

.Y 7' 7 ' 7 '- 7' 7 '7 0,25

N~u hoc sinh lam bai khong thee hu6ng d~n cham nhung dung v~ cho du diem thee tirng cau..

------- HET ---,

</div>

De thi Dap an HK2 khoi 12 BTRE nam 2012

so

BE

<i>f</i>

<i>fx</i>

+

Fx

+

=

o

.

x

=

°

=

=

=

TV

<i>f</i>

= --.

+

lr

1

°

'

=

--

toa

J2

.

<i>B</i>

A

=

M

°

DAN CHAM

N

A

M

.

MON

Gia

'

o

trung

phB thong

a

n

<i>f</i>

<i>et</i>

<i>f</i>

<i>f(x+-+-).dx</i>

mlxl)

<i>=</i>

<i>2J2</i>

-

.

!

.

+

d6

¢'

> [ :

: ~

<i>f</i>

+

<i>f</i>

J

J

1

.

-

---

+

---

so

<i>.</i>

<i>..</i>

<i>...</i>

<i>.</i>