ON TAP HK1 THANG LONG HN

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THPT Thdng Long Hd ndi - Ndm hoc 2010-2011

pi crloNc ON rAp roAN Hec xi I Lop rz

Trtfrng THPT Thang Long Hd ngi - Ndm hoc 2010-2011

Bi6n soqn: Nguydn Thiii phtryng

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PNANI:GIAITICH

Bni f:-Tim m dd hdm sd sau c6 ba di?dm cuc tri I y = mxo *(*, -9)x, +10( m ld tham sd )

l

Biri 2: Cho hdm so : .r,- ' -x + ,,''\ (1) ( rn ld tham so ) l-x

l.Tim m dd hhm sd (l) c6 cuc clai vir cr,rc tidu Vdi girl tri nio cira m rhi khoang cdch giffa hai

didm cuc tri ctia dd thi hdm so (t) birng l0?

Biri3: fim m ddhhm so sau c6 cuc tri r y ,r3 +3mx1+:(r- n')*+mt *nf( m Idtham sdXl).

Vidt phucng trinh ducrng thang di qua hai ctidrn cuc rri cua dd rhi h)m sd ( I ).

Bii 4: Cho hhm so: ' r,- -'vr+4,r-'l 111 x-2 \ /

l.Khrlo sdt su bien thi6n v:\ vd dd thi h)rn sd ( I )

2.Chung minh rlng tich cdc khoang cdch tir mot didm bdt k]' tr€n dd rhi h]m sd ddn cdc

duong ti€m cAn cria n6 ll m6r hang so

Bdri 5: Cho hlm so: .r,= :!_ (( )(1)

"l-l

l.Khrlo s6t su bien thi€n vir vd dd thi (C ) cua hfun so ( I )

2.Yi6t phucng trinh tiip tuyen cl cira (C ) cho d vl hai tiem can cua (C ) cit nhau tao

thlnh m6t tam giiic can

Biri 6: Cho hlm sii: r'= I1 1H;

r*l

Chtmg minh rang : Tich cdc khoang cdch tu mOt clidm Mu (x,,;!o)bdr k'' rhu6c (H) ddn cdc

duong tiOm cAn cua n6 li,r mOt hang so Biri 7: Cho hirm so: "1 = t,tx+! (,,tlurlt,,nr rr,)(1)

J

fim m 0d hhm so (l) cd cuc tri r,i khoirng cdch tU ciidm cuc ridu cua dd thi hlm so (l) den

ti€m cAn xiCn cua n5 bang -Jz{

BiriS: Chohdm so y = xr + nrx + 2 (l)

l Kh6o siit su bi€n thi€n va v0 dd thi cua ham 15 ( t ) m = -3

2 Tim m d6 ti6p tuy€n voi d6 thi hanr rO ( t ) tai A(0,2) tao vdi hai truc toa dQ m6t tam

THPT Thdng Long Hd ndi - Ndm hoc 2010-2011 Biri 9: Cho hdm sd y:?x+3'

x-2

1 KhAo s6t su bidn thiOn vi v€ dd rhi (C ) cria him sd d6 cho

2 Tim tdt ch cdc gi6 tri cira rham sd m dd duong thing y=2x+m c6t (C ) tai hai didm

phAn bi€t mh hai tidp truydn cta (C ) tai hai didm d6 song song vdi

Biri 10: Cho him so y = xt -3xt +4

l.Khrio si{t v}r vE dd thi (C)

2.Goi (d) le duong thing qua A(3;4) vt\ c6 h€ so g6c k.Tim k dd (d) cit (C) tai didm

phan bict A,M,N sao cho hai tiip ruydn cua (C ) rai M vi N vu6ng g6c v6i

Biri 1l:Cho hlm so y= ' i*2 ( l )

2x+3

Khrio sdt su bien thi0n vi vE d<i thi ( I )

1

2 Viet phuong trinh tiip tuyin cua drj thi hlm so (l), bidt

truc tung tai hai didm A ,B cho tam gi6c OAB cAn tai

tiep tuydn d6 c6t

goc toa dQ O

truc hohnh, Bni 12: Cho hdm sd y: x4- (3nt+2).rr + 3m (l) , m lb tham so

I KhAo sdt su bidn thien vI vC dd thi ( I ) vdi m=0

2 Vdi gi6 tri nho ciia m , ducing thAng y=-l cit dd thi hlm so (l ) tai didm phAn biet c6

hohnh dO nh6 hon

Bii 13: Tim gi6 tri ldn nhat vI gi6 tri nho nhat cua him so : /(x)=

?+ rrenf-z.ol

Biri 14: 3.Tim gi6 tri ldn nh6t vd gi6 tri nho nhdt cua hdrn s6 ! = x6 ++(r - t')' trrr[-r;r]

Bii l5: Tim gi6 tri ldn nhAt vd gi6 tri nho nhAt cua hdm s6 ,u = (" + l)Jl - t'

Biri 16: Tim gi6 tri ldn nh6t vd gia tri nhtj nhAt cua hdm s6 y = x

Biri 17: Tim gi6 tri lcrn nh6t va gia tri nho rrhAt cua hdm sd ,u - = ^U*" - Vx e [0;z].

2+cosx Biri l8:Tim gi6 tri nho nhat cua h)nr s0:.r' )1

-*-(0.r.1)

I -X X

nho nhAt cua hdrn sd .v = x + J4 - "'

nho nhAt cua hdm s6 .1, = f + si* * J * rrr"

Bdri 2l :Cho a > 2;b > 3;c > Tim gia tri ldn nhdt cua bidu rhfc:

f= ab,1;4 a 6r,{n _ ':t * ,r,Ji 1 ahc

Biri 19: Tim giri trl l6n

Biri 20: Tim gi6 tri l6n

Biri 20: Tim gi6 tri lon nhat vI girl /'('r) =.r+2+ ),,rrr(l;+-). nhAt vd gid tri

,^

nnat va gra til

) -l

THPT Thdng Long Hd n6i - Ndm hoc 2010-2011

Bii 21: Tim gir{ tri l6n nhat vd gir{ tri nh6 nhat cira him so : / = cos3 x-6cos2 x+9cosx+5

./ = sin3 x - cos 2x + sin x +

Biri2l:Tim gi6 tri ldn nhat vi gid,tri.nhd nhat cira him sd : /(x) = x-er* tren[-t;ol.

PHUONG TRiNH, HE PHUONG TRiNH sAr pHUoNG TRiNH naU vA LocARiT

Biri 1: Tim ci{c gidi

han:-o5' _r ,

,, \ (r0,, _ ,) , c,, _,j,,

t'li$ = '-:;:; :,

z.lim =]"0 ia ';'-i,^ 5'r

Bii 2: Tim dao hdm c[ra cdc hlm so sau:

3 1i* ln(5x+ lF- ln(3x+ t)

r+0 X

l y:5t''(rt +2x? -x+l)

r -r

^ e -e

5 ' v=

e'+e-'

Bii 3: Giii c6c phuong rrinh sau :

t (t-o 6)' +(t +a 6)'=

3.(++Jrs)'*(+-fi)'=oz

t (Jt-')'*(Jt t)' -zJi =o

Bhi 4: GiAi cr{c phuong rrinh sau :

3.4'+9' = 25'

5 4'-l.i-! _rr.2, vi,lit * g

=

T.gfinr'+gl'""'=30

2 .y ="" (r' +2x2 - x +l)

4 )' = e5' (sin x + cos.r)

l.(z+f)"-"*' *(2-S)" " 1- 2.23\+1 -7.21, +7.2, -2:0

2 5t*'+6.5.'-3.5'-r = 52

4 (.6;rG) '+(S-rG) ' =,0

o.(zJI* Jil)"-' *(2 - J, i)"-' = 4Ji

4 (,1;J)'.(#;F)'=oi

6 ( 6_ffi)'.('6.rG)' =,0;

8 3.25'-r +(3x-10).5'-'] +3-x =

14 2log,x + logrr,r+ log, x =

/r

o (za+rs.,6) ' +z(t++.6) ' -r(r-.6)' =' 10 log(x+l) - log ( l-x ): log(2x+3)

I l log.,('-r).*:=1+lns

"t.r 12 tog,(+'+r5.2.+ 27)+2tog,-J-=6 t 13 log,, x = log, (J; - o)

THPT Thdng Long Hd ndi - Ndm hoc 2010-201t

Bii S:Cho phuong trinh: 9r*JF - (o * 2)3r."[} + 2a +t= 0(1) a ld tham sd

l Giei phucng trinh v6i a=4

2 fim a dd phuong trinh (1) c6 nghi€m

Bii 6: Tim m dd phuong trinh: /t"g!"irug, ;t = rn (logo ,' 4) c6 nghiom x e [:z;r )

17 log,(s - t)log, (5'.' -2s) =

19 log, (+.3 - 6)- los, (l' - o) = r

1.4x2 +x.3tr +3r+Ji.2x'3ji +2x+6

3 log.-,(.r'-r)> z

5 (x+l)log] x+(2x+5)log, x+6 > 0 27

7 logo(s' + t)* toe1,,,,) a r i

2'-r +4x-16

x-2

18 tog,

{togn (:'.' - t)} = t

29 4x1-3x+2 * 4x2 +6x+5 _ 42x2 +3x+7 *1

2 log (tr' - sx + 3) >

O s'-'-(:x-g) ,u

Bii 7:Giii ci{c h0 phuong trinh:

,.{tn(l+')-ln(l+ y)=x-y 2.1 to*,(.r'+.v')=s

I x' -l2xy +20y' = g [Z tog , r.+ log, y = 4

^ fr" =5y'-4y I (r'n , ).3, ,' = l

3' j 4' + 2'"' 4.1

lji;=, l*(,'* ,)-6 =o

.r {(t *.v)' = (" -.u)' J los, ,,lo = log, v

llog,x-log,.v=l [ :'+2'=3

^f 3'.2'=972 t i-J1r'l+3=o

t

t,orn g-.v)=2 t i/*, -u/ing,1,=o

n.l'o*,(x'+2x'-3.r-5.u)=3,,, Jff+Jtog.r,=3

[log,(y'+2y'-3y-5x)=; I t-3log.r'2=l

Bii 8:Girii cr{c bAt phucrng trinh:

g'-3

6 log,

Itog, (+' - u)] =

g f l )''*ll"'*l[

t'

":ror't-r]n

\3,

10 log._,(x+l)> log,,

9

I

,l

,>l

_,(x+l)

On thi hoc ki I

>4

-1-THPT Thdng Long Hd nili - Ndm hoc 2010-2011

psAn u: HiNn Hec

Biri l:Cho khdi ch6p ddu S.ABCD c6 AB-a, g6c gifia mdt b€n vi mat ddy bang 600 Tinh thd

tfch khOi ch6p S.ABCD theo a

Dii 2:cho khdi ch6p S.ABC c6 ddy ABC l) tam gi6c vu6ng tai A, AR=a, AC = aJ1, m6r b€n

!SBg)_ld tam gi6c ddu vi vuong gdc v6i mat phang ddy Ttuh theo a rhd tich khdi ch6p

S.ABC

Bii 3:Cho ling tru tam giiic ABC.AIB'C' cd tdt cA c6c canh d6y ddu bang a, g6c tao b&i canh

b€n vi mat di{y la 600 v} hinh chieu H cua dinh A l€n mp(A'B'C') trirnf vditrung didm ctra

c4nh B'C' T(nh th6 tich kh6i lang tru ABC.A'B'C'.

BAi 4:Cho hinh hOp dung ABCD.A'B'C'D' cd ddy ABCD lI hinh thoi canh a G6c

ffiouG69 sfua ou,rng.h6o A'c vir mit phing d?y bang 600.Tinh tnd tich rri"r, nOp ia.

dinh vd tfnh dd dli doan vuong g6c chung cua A'C vI BB'

Biri S:Cho hinh ch6p S.ABCD c6 cl6y ABCD ld nua luc gi6c ddu vdi AD=2a,AB=Bc-CD-a,

SA I(ABCD);S.q = oJT.Vot rnlr phing (P) di qua A vl vu6ng g6c vdi SD cit SB, SC,SD tai

B',C',D'.Tinh thd tich khdi ch6p AD'DBB',X6c dinh tAm vh br{n kinh m6t cdu ngoai tidp

hinh ch6p

Blri 6:Cho ling trg clfng ABC.A'B'C' c(r tat cA c/rc canh ddu bing a.Goi M le rrung didm

AA'.Tfnh thtj tfch khoi tri cli€n BMB'C' thco a vi\ chfng minh rang BM vu6ng g6c vdi b'C

Bii 7: Cho hinh ch6gr S.ABCD c6 tliy SA I(ABCD):Str = oJ1 Xac clinh ram vi) bitn

ABCD le hinh vu6ng canh a, canh b€n

kinh mit cdu ngoai tiep hinh ch6p S.ABCD

Bii 8: Cho hinh ch6p S.ABCD c6 diry ABCD lI hinh vuOng canh a, SA=SB=AB , mar phing

(SAB) vu6ng g6c vdi rnat phing (ABCD) Tfnh brin kfnh mdt cdu ngoai tidp hinh ch6p S.ABCD

Bii 9: Cho hinh ch6p S.ABCD c6 diy ABCD ll hinh chfr nhAt vI Sl r(ABCD).Goi B',C',D'

ldn luot l) hinh chieu vuong g6c cua A tren SB,SC,SD

l Chtnrg minh ciic diCm A,B',C'.D'clOng phang

2 Chrnrg minh 7 didm A.B,C,D,B',C',D' cing thu6c mOt m4t cdu

Biri l0: Cho hinh tru c(r birn kfnh diry bing R, thidt cliOn qua truc cua hinh tru ll mor hinh

vu6ng

l Tinh diOn tfch vir thd tich hinh c.,iu ngoai tiip hinh tru

2 MQt mat ph.ang (P) song song vtii truc cua hinh tru cit driy hinh tru theo rn6t dAy cung

c6 dO dli bing b:in kfnh driy hinh tru "finh cliOn tich ciic thiet dien cria h)nh tru ua ninn

THPT Thdng Long Hd ndi - Ndm hoc 2010-2011

Bii 11: Cho hinh tru c6 bdn kinh dr{y bang R,chidu cao Rr6

1 Tinh diOn tich xung quanh vi di€n tich toin phdn cfia hinh tru

2.Tinh thd tich ctra khdi tru girli han boi hinh tru

3.Ctro hai didm A vh B ldn lucn nim tr€n hai duong trdn d6y cho g6c giffa AB vi truc cira

hinh tru blng 300.Tfnh khoang ciich gifra AB vd rruc ctra hinh tru

Biri ?: Cho tam gi6c ABC ddu canh a vd (P) ld mit phEng qua BC vd vuong g6c mp(ABC)

Gqi (C) lh duong trdn dudng kinh BC vl nam mp(P)

l.Tinhbr{nkinhm[tcdudiquaducrngtrdn(C)vhdidmA.

2.M0t hinh n6n ngoai tiep mlt cdu n5i [r'On cho cdc tidp didm gifra hinh n6n vh mit cdu

lh duong trbn (C).Tinh thd tich cua khoi n(rn

Bii 13: Cho hinh n6n (^tD c6 bdn kinh driy R ducrng cao SO Gqi (P) ld mat phing vuong g6c

vdi SO tai O' sao choSO'= lt, M6t rlat phing qua truc hinh n6n c6t phdn khdi n6n (^rD

3

nam gifra (P) vl d6y hinh n6n theo thiet (lien ll hinh tf giric c6 hai duong ch6o vuong g6c

Tinh thd tich phdn hinh n6n (^il) nam gita rnp(P) vi mit phing chrla d6y ciia hinh n6n (^il)

-THPT Thdng Long Hd nili - Ndm hoc 2010-2AtI

A\

nE rHI HoC ri I LoP 12 nnON ToAN

THOI GIAN : 90 PHUT

(Oay li dA thi cia nim hoc 2009-ZO1O e6 HS tham khio)

CAu 1(2.5d): Cho hhm so : -v = x4 - 6x2 + -5

a) Khio s6t su bidn thi€n vh vE cld thi (C ) cria hlm sd

b) Tim m dd phuong trinh xa -6.rr -2m=0 c6 nghi€m phAn bi€t

Chu2Q d\z GiAi crlc phuong trinh:

I) (8-rJ7)' +(s+rJ7)' = ro

2) logn (n' - t)logn (9.'*2 -81) =

CAu 3(1d): Tim gi6 tri ldn nhat vi\ giri tri nho nhat cua hirm sd -y - x + Jr=t

CAU 4(2d):Cho hinh ch(rp S.ABCD c(r day ABCD le hinh vu6ng canh 2a, SA=a !

SB = oJl A mp(S,ll) L mp(ABCD) ,goi H,K ldn luor ll trung didm ciia c6c canh AB,BC

Tfnh theo a thd tfch cua khoi ch6p S.BI-ll)K X:ic clinh tArn vI tfnh bi{n kinh mf,t cdu ngoai

tidp hinh ch6p S.AHOJ O l)r giao cliCnr cua AC vl BD, J l) trung didm AD.

CAu S(2d):Cho hinh hop cltrng ABCD.A'lJ'C'D' c6 dAy ll hinh thoi canh a, g6c fEd=60",

g6c gifra mat phing (A'BD) vi mit phiing cliry blng 600.Tfnh theo a thd tfch hinh h6p T(nh theo a khoang crlch til dudng thing CD' din mAt phing (A'BD)

Cdu 6(0.5d):Giei hc phuong trinh:

I ,t xl+l

] " =t"*'