Thi thu DH-Toan D-2012-lan 2- Le Xoay

X6c dinh m AC AO thi hdm s6 1f c6 hai diOm cr,rc dai, cuc titiu nim ve hai phia cira tnrc tung.. Tim s6 nguy€n ducrng n nho nhAt sao cho: trong khai triOn l + x'theo cOng thtic nhi thric

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\ \ rRtroNG rHpT rp xoav on rnr

KHAO sAt cnAr L{toNG Kr{or t2 -LAN rr

Ndrn hsc 201r'2a12

rndi eion,Yilp:rT?til"rnuk3;i", giao di)

Cf,u 1:

ChohdmsO y= mxt -3xz +(*'-3m+2)x+4 (1)

1 Kh&o s6t su bi6n thi€n vd vE d6 thi hnm sti dA cho vdi m = 1.

2 X6c dinh m AC AO thi hdm s6 1f) c6 hai diOm cr,rc dai, cuc titiu nim ve hai phia cira tnrc tung

Ciu2l.

t Gi6i phuong trinh: cos2 x = (1+ sinx)(sin3x - 2sin x + l) .

lZ*' -9y3 = (x - y)( xy -I)

2 Giai he phucrng trinh: j , ^ u ; "." '

l*'-3'Y* Y" =-l

Ciu 3:

1 Giei phuirngtrinh: x13]5-1 = l1l.frIl+Jts-rlf"-rl

2 Tim s6 nguy€n ducrng n nho nhAt sao cho: trong khai triOn (l + x)'theo cOng thtic nhi thric Newton, c6 hai sO hpng Ueri titip mA ry lQ cria hai hQ s0 bing 5i9

Cfiu 4:

d2; 2x* y + 1 : 0.vi di€m M (1;.- 1) X6c dinh to4 d$ di0m A thuQc d1 vd B thuQc d2 sao

cho M li trung di6m cua dopn thbng AB.

2 Cho hinh ch6p S.ABC c6 chi c4nh b€n dAu nghi0ng v6i d6y mQt g6c 45' D6y la tam gi6c ABC c6 AB = AC = a; eEC = ,q,eB = a .*H ld hinh chi6u cira S l€n (ABC)

a CMR: HA: HB = HC = HS? Tinh SH?

b Tinh th6 tich hinh ch6p S.ABC

C6u 5: Bitlt x, y,z e R;x23;y> 4;z> 5 Chtmg minh rlng :

ytJi-z**t.[y-+nryJl-s._L* xyz =tE- 4-tG I - l_

http://www.haimathlx.violet.vn

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BAp Ax

EE Tlu xnAo sar cnAr iuql{c xlr6r rz

MON: rOAr.r- rH6t n, o

V5i rn = t Ta c6 hdm s5: y = xt -3x2 + 4

Cdc gi5'i han: lim y = N -crr; lim y = a[

f,++€

Sg bitln thi€n:

r^)

V = 3x- -6x

v'-0<>1"=o

- l 1

L^_L Hdm s6 d0ng bi6n tr€n (-oo; 0) vd (2; +m) Hdrn sO nghich bi6n tr€n (0; 2)

Hdm s6 dfi CE tqiy = 0; yio:4

= O

0,25

Bing bi6n thi€n

0,25

4+*

Eths cft oy tpi (0; 4)

cdt ox tai (-1 ;0); (2;0) Nhfln I (1;2) ldm t6m <ftii xrirrg

f(x)=x^3-3-x^2i.4t : : :, ,,::t.:i

| :/

'."-:- - i*-: -t : l i:r

.,-.,: : 1 I , I I t

\J: : ! :

*_- '-: -

a-

j:-*, i l

\r, : l

\:,l gfr -.

i 1: I i

ii: r!

!l

li

i, i, i i ili:i :

-i.-:-:; -: -;-, -i

*-: r | : I

-_i _,1: : r/

i\.;r ri

- j .-. +-.j-.Jj.-,

-i I t! 2r','t I

tl

*-r : -i., i , ,, , .i:.- -:

. . 1 i.-.i ,,.: , i: :

ol

-zl -.: -:- i-,,.-:_ :

ti

0,25

!'=3mx2 -6x+{m2 -3m+2)

D€ ilths (l) c6 cuc dai, cgc t

tr6i dAu.

thoi miny€u cAu bdi toa

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()<

lm*0

*3m+2) <0

*[

v0y

m<0

1<m<2

m e (-*;0) U(1;2)

cost e(l

It lr

I = (1 + sin x)(sin3r - 2sinx + t)

- sin 2 .r) = (l + sin x)(sin 3.r - 2 sin lc + l)

+sinx=0 -sinx=sin3x-2sin.r+1 lsin x = -l

cri lsin 3x = sin x

r,

lr=-'72

elx=tr

L.=%*

+ k2r

ln,/

/2 (k;leZ)

<) x' = 8/'

o x =2y (3) Th6 (3) vdo (2): - y' = -t <+ y = +1 VOv h0 tl6 cho c6 2

y =1> x=2

/=-l)x=-2

Edt #; = u;Ji]l =, e s u;v < 2)

Ta duoc: v2 +l + 3u = | + 3u + uv DK: 1 <x{5

v2 +3u-3v-uv=0

(u -v)(3 - v) = 0

fu=v

.-[v=3

Do rti6u ki6n n6n u _ v +n/j- = .f,J <+ 5 _ x = x _f *,, =l-(til6

D6p s6: nghi€m pt ld x = 3

0,25

(1)

(2)

= (x - y)(4xy -t)

2

- l

y r

4xy + x2 -3xy + y2)

y)(x' + xy- y')

Gi6i he: {':' -"'t2

I.r - Jxy + rh6 (2) vdo (t):

2x3 -9y3 = (r - yX

e 2xi -9y3 = (x

-0,25

0,25

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3.2 lal'

1.I Theo cOng thirc nhi thrlc Newton

(l + x)' = Cl + C)x + Clx2 + + C!xk

2 h$ s6 ctra 2 s6 hpng li€n ti€p lit: C!;C!.l (0<f <n;keZ)

0,25\

Theo gii thi€t:

ck

+Xdt: -'

c:*' 9 kt(n-k)r 9 (k+1)!(n-r-1)!

e9(k+l) = 5(n-k)

elt-zk+l+4k+4

5

0,25

n ld s0 nguyen ducrng nho nh6t = Gk ! O ld s5 nguy€n duong nh6 nh6t

=,t=4=n=13

0,25

fk+t S

*Xdt: -n' = "

c:e

ES: z: l3

Tuong t.u c6 k=8, n=l3

0r25

1d Vi I e d, + A(tr;-t, *1)

B e d, + B(t2;2t, +l)

0,25

tL-1,=1,^-l

Theo ycbt - AM = MB

= 1- It, =Zt, 't '2+Z ={,, Ir' -0

-t

0,25

SA c6 hinh chi6u h HA tr€n (ABC)

'=>

96c gig_a SA v,q (ABC) l4 &4i?

= 45'

=> ASAH vu6ng cdn t4i H => HA = HS Tuong t.u : HB = HS; HC = HS

VQy HA: HB = HC: HS Theo tr€n -> H ld tdm duOng tr&n ngo4i ti6p

AABC;iheo dinh ly Sin: AB/SinC{AH

=> AH = a(Zsino):> SH: a(2sino) 4.2b

I

V*u, =

iSH.SMBC

l^1

S-ac =

=en.AC.sinBAC 22 =*a'.sin(l80" -2a)

1

=!a2.sin2r;,

2-" '-"'-*

4,25

0,25

Ar25

0,25

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I

vsnc = +#:'z sin2a= 1 o, ro, o

viitrai -G-3 xyz *F *B

?/,\ Jt-X6t hdm s6: f Q) = tf e 2 a;a> 0) ; a ld hing

sd.

-f'(t) = BT:

,/2o

*Jt-3,"ly-4 J= | I I

*

-; * - , * *;-

= ui+ V.ft (Ddu ':' xtty rakhi x=6; 58; z:10)

n- .Jl .,[ru .Jo

-x - 6' y - I

f t:

',1 Z- ) _ V:

zl0

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Dung lượng	3,5 MB