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NGUYEN SY DlrC - LE DAI HAI - NGUYEN PHUC LONG
TU LUVEN • •
Vi Olympic
TOAN 12 TAP 2
•
[ Phien ban 2.0 ]
NHA XUAT BAN GIAO Dl,JC Vll;T NAM ----------------------------------------------------------------------
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Chiu trach nhicm xu~t Mn:
Chu tjch H¢i dOng Thanh vien NGU'T NGO TRAN Al
Tang Giam d6c kiem T6ng bien t~p GS.TS VO VAN HUNG
T6 ch(lc ban thao va chiu trach nhicm n(Ji dung:
Ph6 TOng bien t~p NGO ANH TUYtT
Giam d6c COng ty CP Sach dan t¢c HA THI HAI YtN
Bi6n t~p n(Ji dung:
VO MAI HU'ONG
Bi6n t~p mT thu~t:
NGUYi=N THANH LONG
Trinh bay bla:
DANG HONG QUAN
Thi!Jt k!J sach va ch!J ban:
VO MINH HOANG
COng ty c6 phAn sach dlln t¢c - Nha xuat ban Giao dl,IC Vi$t Nam giCr quyen cOng b6 tac pMm
TU SACH VIOL YMPIC - TV' LuveN VIOL YMPIC - TOAN 12 TAP 2 - PHl~N BAN 2.0
Mi sO: TZT19T4-CDT
s6 DKKH xuit ban : 214 - 2014/CXB/70-125/GD
In 3000 ban, (00: 51 ), khO: 17 x 24cm, T;;ii : Xi nghiE;lp ban do 1 - BQ Qu6c PhOng
Dia chi: Xuan Dinh - TCt Liem - Ha NQi
In xong va n(>p IU\J chi~u thang 9 n~m 2014
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LOINOIBAU , Cac em h9c sinh yeu quy !
t. ~ '<.- (tu9c thi giai toan qua Internet- ViOlympic la CUQC thi qu6c gia do 89 Giao dl,JC va ~ ,Patj;t<?O to chl.fc, T~p doan FPT, TrU'6'ng 89i h9c FPT thl,J'c hi~m hang nam, bat dau tU> 0
nam hQC 2008- 2009. TU> nam hQC 2011 - 2012, CUQC thi ViOlympic con 19 vong thi, tU> vong 1 den vong 9 la cac vong thi tl,J' luy$n, tU> vong 10 den vong 19 la cac vong thi cac cap. .
f)e hQC sinh lam quen vai d9ng bai thi hap dan, kfch thfch tU' duy Va luy$n t$p trU'ac khi thi tren may tf nh, Tieu ban n9i dung - Ban to chl.fc Qu6c gia to chl.fc
"' bien so9n b9 sach "Tl,P luy$n ViOlympic Toan - Phien ban 2.0". 89 sach nay g6m 24 cu6n tU> lap 1 cten lap 12, moi lap c6 hai t$p vai cau true 19 vong thi tU'O'ng Ling vai 19 Vong thi tren trang WWW. vio/ympic. vn, moi vong thi tU'O'ng Ling vai hai tuan hQC theo phan ph6i chU'ang trlnh cua 89 Giao dl,JC va Dao t90.
89 sach "Tl,P luy$n ViOlympic Toan - Phien ban 2.0" dU'Q'C phat hanh d6ng thai vai bQ sach "Tl,P luy$n ViOlympic Toan" 35 vong thi. Cac em c6 the su d1,Jng ca hai bQ sach de ren luyt;in man Toan n6i chung va thi ViOlympic n6i rieng.
Khi lam xong moi vong thi trong cu6n sach nay, cac em c6 the truy c~p Internet, vao dja chi: www.violympic.vn de dl,J' thi. Khi vao trang nay, cac em can dQC kT phan Tr<;>' giup va lam theo hU'ang dan de c6 the thi dU'Q'C t6t nhat.
Xin cam an Cong ty Co phan Sach dan toe - Nha xuat ban Giao dl,Jc Vi$t Nam da t90 dieu ki$n de cu6n sach tai dU'Q'C cac em.
Chuc cac em h9c man Toan ngay cang say me han, tien b9 han va d9t ket qua ~o nhat trong cu9c thi ViOlympic cOng nhU' trong h9c t$p.
\J Cac y kien g6p y cha tac gia, cac thay co giao va cac b~c phl,l huynh, hQC sinh CO the gtJii Ve horn thU': vio/[email protected]. vn ho$C gtJii Ve dja chf:
Phong ViOlympic Truong 89i h9c FPT s6 8 Ton That Thuyet- My rnnh - TU> Liem - Ha Noi.
~ cAc TAC GIA .
;;:-) ~
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HU'ONG DAN SO' Dl)NG SACH
I. HU'ONG DAN CHUNG
Tl,P luy~n ViOlympic Toan 12 t~p 1 - Phien ban 2.0 c6 9 vong thi, tlJ> vong 1
den vong 9, moi vong thi gom hai de thi tU'O'ng IYng v&i kl thi tv luy$n tren trang
www.violympic.vn.
Tl,P luy~n ViOlympic Toan 12 t~p 2 - Phien ban 2.0 c6 10 vong thi , tlJ> vong 10
den vong 19. TU> vong 10 den vong 16, moi vong gom hai de thi tU'O'ng Cmg v&i
kl thi dp trU'c'Yng va cflp huy$n tren trang www.violympic.vn . TU> vong 17 den
vong 19, moi vong c6 1 de thi tU'O'ng IYng v&i kl thi cap tfnh va cflp quoc gia tren
trang www.violympic.vn .
Cac em can dQC kT d~ xac dinh yeu cau cua tung bai thi , dQC them hU'&ng l
dan 6' mt,JC II doi v&i hlnh thlYc thi c6 yeu cau phlYc tc;ip.
Doi v&i cac hlnh thlYc thi: Ch<;>n dap an dung, Dien ket qua vao cho " ...... ", VU'<;>'t chU'6'ng ng~i v~t. Coe Vang tai ba, Dinh nui tri tu~ cac em lam bai
tn,.l'c tiep tren de.
£)~ thu~n ti$n cho vi$c SU dt,Jng sach va ap dt,Jng cho bai thi tren web,
hlnh thlYc tra lc'Yi cac dc;ing bai thi: Di tim kho bau, C~p bang nhau, Sap xep Se dU'Q'C hU'&ng dan chi tiet hO'n:
11. HU'ONG DAN MQT 50 BAI THI
1. DI TiM KHO BAU
Yeu c~u: Em hay giup chu thQ' mo tlm dU'ang di trong me cung de den dU'Q'C 0 CO kho bau bang each giai cac bai toan ~n trong cac 0 tren dU'ang di da ch9n.
81..F&c 1: Tim dU'c'Yng di trong me cung cho chu thq m6.
Dung but ve m(>t dU'c'Yng di qua cac 6, xuat phat tlJ> vi trf cua 6 c6 chu thq m6
den vi trf 6 chlYa kho bau .
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A~ Chu y: Khong dU'Q'c ve vao cac 6 c6 chLi'a tU'ang da ~-
Vid1,1:
BLP&c 2: Giai cac bai toan g(lp phai tren dU'ang di da ch9n.
- Xac d!nh vi tri cac 6 trong bang chLi'a cac bai toan tren dU'ang di da ve. Trong hlnh ve tren, cac bai toan g(lp tren dU'ang di da ve theo thLi' tl,l' la
(dem theo thLi' tl,l' tu tren xu6ng dU'&i , tu trai sang phai de xac d!nh phai lam
bai toan nao):
Bai toan 1 ; Bai toan 5; Bai toan 8
(TU'ang Li'ng trong sach se la Cau 1; Cau 5; Cau 8)
- Giai cac bai toan trong cac 6 da xac djnh roi diem ket qua vao cho " .... . "
ho(lc ch9n dap an dung tuy thu('>c vao dc;ing bai toan tU'O'ng (Jing .
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Bai toan 1. Cho ham so f(x) c6 dQo ham la: f '(x) = x ( x + 1)2 ( x -2)4, v&i mQi x E JR.
Khi d6 so diem Cl,J'C tieu cua ham so la .......... .. ...... .
Dap so: 1
, Bai toan 5. DU'ang thang y = 3x + m la tiep tuyen cua dlJ'ang cong y = x3 + 2
khi m E { ...... }.
Dap so: O; 4
Bai toan 8. So m~t phang doi xt'.Png cua hlnh l~p phll'O'ng la ... . ..... .. ... . .... .
Dap so: 9
2. C~P BANG NHAU
Yeu cau: Em hay tim trong bang sau cac c~p 6 chUia cac k~t qua, gia trj, ... bang nhau ho~c dong nh~t v6'i nhau.
BU'&c 1: Tfnh nham ho$c lam tren giay nhap de tlm cac ket qua 6' tat ca cac 6.
BU'&c 2: Lan lll'qt ch9n cac c$p 6 cht'.Pa cac ket qua gia tr!, .. . bang nhau ho$c dong nhat v&i nhau.
BU'&c 3: Lan IU'qt di~n so tht'.P tl,J' cho cac c$p 6 d6.
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' Vi dv: Em hay tim trong bang sau cac c<;lp 6 chl'.ra cac ket qua, gia tr!, .. . ' bang nhau ho<;lc dong nhat v&i nhau.
Gia tr! cua x thoa man: Gia tr! cua x thoa man: Gia tr! cua x thoa man: x3 - 5x2 + 6x
= 0 7x2 - 496-2x = 0 g2x + 2.9x+1 = 40
ln(x - 1)
0 f) • X= 3 x = log9 2 [ x =-6
X= 2
0 • f)
3. SAP XEP
Yeu cau: Em hay sap xep cac ket qua, gia trj, ... trong cac 6 cua bang sau theo thll' tl! gia tri tang dAn.
BLP&c 1: Tfnh nh~m ho<;lc lam tren giay nhap d~ tlm cac ket qua a tat ca cac 6.
BLP&c 2: Sap xep cac ket qua d6 theo gia tr! tang dan.
BLP&c 3: Dien so thl'.r tl,l' lien tiep theo day so tl,l' nhien vao cac 6 da dU'Q'C sap xep theo thl'.r tl,l' gia tr! tang dan, 6 c6 gia tr! nh6 nhat trong bang dU'qc danh so 1.
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----------------------- ---------------------------------- ------- ------- ... , ' ' Vi d11: Em hay s~p x~p cac k~t qua, gia trj, ... trong cac 6 cua bang sau theo '
thli tl)' gia tr! tang dtin .
-
Gia tr! nh6 nhat cua m Gia tr! nh6 nhat Gia tr! l&n nhat
de phLI'ang trlnh cua ham s6 cua ham s6
(x - 1)(x- 3)(x+5)(x+ 7) = 2m y = cos3x + cos2x + 3 cos x y =-X4 + 2x2
c6 nghi$m tren do9n [3 ; 4]
8 • • Gia tr! nh6 nhat Nghi$m cua Nghi$m cua
cua ham s6 phU'ang trlnh phU'ang trlnh
y = cos3x - 3 cos x 22x+1 = 42x+1 12x + gx - 6.1 6x = 0
e 0 0
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PHAN 1. CAC BE TU LUYEN . .
Web t'/ lu~n
Em hay dien ket qua thich hctp vao cho " ...... " trong moi
cau sau.
C A 1 s .< d' ~ t . • h ' ,:. 4 b 2 ( 0 b 0) I ' au . o 1em Cl,PC n cua am so y = ax + x + c a > , > a ... ... ....... .
Cau 2. PhU'O'ng trinh 2x + 2x-1 + 2x-2 = 3x - 3x-1 + 3x-2 co nghi$m x = ......... .
Cau 3. M(>t hinh tn,J co dU'ang tron (01) va dU'ang tron (02) la hai day. M(>t 1llnh I
non co dlnh la 0 1 va day la dU'<Yng tron (02 ) . Khi do ti so gifra the tfch
khoi tn,.1 va khoi non tren la .... .. ... .
Cau 4. Cho khoi chop S.ABC co the tfch bang 120, M la trung diem cua SC, N la trung diem cua BM. Khi do the tfch cua khoi chop N.ABC la .. ......... . ( dvtt). ,
CaAu S. G'' t . h' h"t • h ' ... sinx+2cosx+1 1. 1a n n o n a cua am so y = a .... .......... . · sinx+cosx+2
C A 6 H · " 2x + m I A d" b'" t A tA • d' h kh' au . am so y = !?-: uon ong 1en ren <;ip xac !n 1 m = ..... .. ... . -vx2 +1
Cau 7. T~p nghi$m cua phU'ang trlnh
log3 (x2 + 3x + 2)+ log3 (x2 +?x+12) = 1+log3 8
las={ ......... ; .. .... ... }. (Cac gia tri ngan each nhau b6'i dflu ";")
Cau 8. Gia tri l&n nhat cua ham so y = x.J1 - x2 la ............ .
Cau 9. Cho do thi (C): y = 2x + 1
va dU'ang thang dm: y = -x + m (m > 0). x+2
De dm cat (C) t<;ii hai diem phan bi$t A, B sao cha AB= 2.Ji4 thl m = ... . . ' ------------------------------------ ------------------------ ----------'
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