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: TRAN DUY SO' - PHAM 8VC TAI - PHAM TH! MINH TUYi;N I

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TU LUVEN • •

ViOlym·pic

TOAN 11 TAP 1

•

[ Phien ban 2.0 ]

NHA XUAT BAN GIAO Dl)C Vll;T NAM '----------------------- ----- ----------------- ------ ------------------- ;

    

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Chiu trach nhi~m xu§t bafl:

Chu tjch H¢i dbng Thanh vien NGU'T t-JGC TRAN Al

Tong Giam d6c kiem Tong bien t~p GS.TS VO VAN HUNG

T6 chlfc Mn th8o va chiu trach nhi~m n()i dung:

Ph6 Tong bien t~p NGO ANH TUYi;T

Giam d6c COng ty CP Sach d~n t¢c HA THI HAI Y~N

BitJn t~p n()i dung:

VO MAI HU'ONG

BitJn t~p mi thu~t:

NGUYtN THANH LONG

Trinh bay bia:

DANG HONG QUAN

Thief ke sach va ch!J Mn:

VO MINH HOANG

COng ty Co phftn 8ach dfm t¢c - Nha xu~t ban Giao d1,1c Viet Nam gifr quyen cOng b6 tac pham

TU sAcH VIOL YMPIC - TV' LuveN VIOL YMPIC - TOAN 11 TAP 1 - PHli;N BAN 2.0

Ma s6 : TYT12T4-CDT

so DKKH xuit ban: 214-2014/CXB/67-125/GD

In 3000 Mn, (00: 51), kho : 17 x 24cm, T~i : Xf nghiep Mn d6 1 - 8¢ Ou6c PhOng

Dia chi : Xu~n Dinh - TL1 Liem - Ha N¢i

In xong va n¢p IU'u chi~u thang 9 nam 2014 '~---------------- - ------------ - --------- - ------------ - - - -- - -- - - - -- - - - - ~

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LOINOIBAU Cac em h9c sinh yeu quy !

Cu(>c thi giai toan qua Internet - ViOlympic la CUQC thi quoc gia do BQ Giao d1,.1c va Dao t<,io to chU>c, T$p doan FPT, TrU'6'ng D<,ii hQc FPTthl,J'C hi$n hang nam, bat dau tt) nam hQC 2008-2009. Tt) nam hQC 2011 - 2012, CUQC thi ViOlympic con 19 vong thi , tt) vong 1 den vong 9 la cac vong thi tl,J' luy$n , tt) vong 10 den vong 19 la cac vong thi cac cap.

De hQC sinh lam quen v&i d<,ing bai thi hap dan, kfch thfch tU' duy va luy$n tc;ip trU'&c khi thi tren may tfnh , Tieu ban n(>i dung - Ban t6 chU>c Quoc gia t6 chU>c bien so<,in b(> sach "Tl,J' luy$n ViOlympic Toan - Phien ban 2.0". B(> sach nay gom 24 cuon tt) l&p 1 den l&p 12, moi l&p c6 hai tc;ip v&i cau true 19 vong thi tU'ong U>ng v&i 19 vong thi tren trang www.violympic.vn, moi vong thi tU'ang U>ng v&i hai tuan hQC theo phan phoi ChU'ong trlnh cua BQ Giao d1,.1c va Dao t<,iO.

B(> sach "Tl,J' luy~n ViOlympic Toan - Phien ban 2.0" dU'Q'c phat hanh dong thc'Yi v&i b(> sach "Tl,J' luy~n ViOlympic Toan" 35 vong thi. Cac em c6 the s& d1,.1ng ca hai b(> sach de ren luy~n men Toan n6i chung va thi ViOlympic n6i rieng .

Khi lam xong moi vong thi trong cuon 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 TfQ' giup va lam theo hU'6'ng dan de c6 the thi dU'Q'C tot nhat.

Xin cam on Cong ty C6 phan Sach dan t(>c - Nha xuat ban Giao d1,.1c Vi~t Nam da t<,iO dieu ki$n de CUOn sach t6'i dU'Q'C CaC em.

Chuc cac em hQc mon Toan ngay cang say me hon, tien b(> hon va d<,it ket qua

C o nhat trong cu(>c thi ViOlympic cOng nhU' trong hoc tc;ip .

Cac y kien g6p y cho tac gia , cac thay co giao va cac b$c ph1,.1 huynh, hQC sinh CO the glJi1 Ve horn thU': vio/ympic@moet.edu. vn hoc;ic glJii ve dja chi:

Phong ViOlympic TrLI'<'Yng D<,ii hQC FPT so 8 Ton That Thuyet - My Dlnh - Tt) Liem - Ha N(>i.

CACTAC GIA

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HU'ONG DAN SO' DVNG sAcH

I. HU'6'NG DAN CHUNG

Tlf luy~n ViOlympic Toan 11 t~p 1 - Phien ban 2.0 c6 9 vong thi, tu vong 1 den vong 9, moi vong thi g6m hai de thi tU'O'ng (mg v6'i kl thi tl,I' luy~n tren trang www.violympic.vn.

Tlf luy~n ViOlympic Toan 11 t~p 2 - Phien ban 2.0 c6 10 vong thi , tLi' vong 10 den vong 19. Tu vong 10 den vong 16, moi vong g6m hai de thi tU'ang (mg v6'i

kl thi cap trU'6'ng va cap huy~n tren trang www.violympic.vn . TLi' vong 17 den vong 19, moi v6ng c6 1 de thi tU'O'ng (mg v6'i kl thi cap tlnh va cap qu6c gia tren

trang www.violympic.vn.

Cac em can d9c kT de xac djnh yeu cau cua tLi'ng bai thi , d<;>c them hU'6'ng dan & ml)C II d6i v6'i hlnh th(rc thi c6 yeu cau ph(rc tc;tp.

D6i v6'i cac hlnh thuc thi: Ch9n dap an dung, E>il!n ket qua vao cho " ...... ", VU'Q't chU'6'ng ng~i v~t, Coe Vang tai ba, E>inh nui tri tu~. cac em lam bai

trvc tiep tren de.

De thu~n ti~n cho vi~c sU> dt,Jng sach va ap d1,mg cho bai thi tren web, hlnh th(rc tra 16'i cac dc;ing bai thi: E>i tim kho bau, C~p bang nhau, Seip xep se dU'qc hU'&n§ dan chi tiet hO'n:

11. HU'ONG DAN MQT SO BAI THI

1. £>1 TiM KHO BAU

Yeu cau: Em hay giup chu thQ' mo tim dU'O>ng 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'O>ng di da ch9n.

81.J'&c 1: Tlm dU'6'ng di trong me cung cho chu thq m6.

Dung but ve m(>t dU'6'ng di qua cac 6, xuat phat tu Vi trf cua 6 c6 chu thq m6

aim vi trf 6 ch(ra kho bau.

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Chu y: Khong dU'Q'C ve vao cac o c6 chU>a tU'erng da

Vi d1,1:

BLJ'&c 2: Giai cac bai toan g$p phai tren dU'erng di da ch9n.

- Xac djnh vi trf cac o trong bang chU>a cac bai toan tren dU'erng di da ve.

Trang hlnh ve tren, cac bai toan g$p tren dU'erng di da ve theo thU> ti,./' la

(dem theo thU> tv tU> tren xu6ng dU'&i, tU> trai sang phai de xac djnh phai lam

bai toan nao ):

Bai toan 1; Bai toan 5; Bai toan 8

(TU'ang U>ng trong sach se la Cau 1; Cau 5; Cau 8)

- Giai cac bai toan trong cac 6 da xac djnh roi di~n ket qua vao cho " ..... "

ho$c chc;>n dap an dung tuy thu¢c vao dc;ing bai toan tU'O'ng (Jing.

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... ------ ---- --- --- ---- ----------------- ------------------------- ------- ... , ' ' Bai toan 1. '

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Dieu ki$n xac djnh cua phU'ang trinh ~ + .J3 - x < - 2x la:

~ X E [1 ; 3) @ XE 0

Bai toan 5.

@) X E (3 ; + oo ) @ XE( - oo; Q)

Dapan: ~

Cho tam giac ABC c6 AB = 18cm; BC = 21 cm. Tren tia doi cua tia AB, lay diem M sao cho AM = 6cm. 8U'6'ng thang qua M va song song v&i BC cat AC tc;i i N. Tinh d(> dai doc;in thang MN.

Dap s6: 7cm Bai toan 8.

T$p nghi$m cua phU'ang trinh (x + 5)(2- x) = 3~x2 + 3x la S = { .. .. .. . ; ... .. ... } (Viet cac phan tif cua t~p hQ'p S theo th& tv gia trj tang dan, ngan each nhau b&i dau ";'?

Dap s6: {-4; 1} 2. C~P BANG NHAU

Yeu cau: Em hay tim trong bang sau cac c~p 6 ch(ra cac ket qua, gia trj, ... bang nhau ho~c d6ng nh~t v6'i nhau.

BU'&c 1: Tinh nham ho~c lam tren giay nhap de tim cac ket qua & tat ca cac 6.

Booe 2: Lan IU'Q't chon cac c~p 6 chl.Pa cac ket qua gia tri, ... bang nhau ho~c dong nhat v&i nhau.

Booe 3: Lan IU'Q't dien so thl.P tl,I' cho cac c~p 6 d6.

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----------------------------- ----- --------------- ------------- -------- ... , ' ' Vi dlJ: Em hay tlm trong bang sau cac c~p 6 chtJia cac ket qua, gia tri, ... '

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bang nhau ho~c a6ng nhcfit v&i nhau.

sin3x tana + tanb . 6 x 6 x

sin -+cos -2 2

0 • • 3sinx-4sin 3 x 1 3 . 2 sin(a+b)

--Sin X 4 cosa.cosb

0 • • 3. SAP xi=P

Yeu cilu: Em hay sap xep cac ket qua, gia tri 1 ••• trong cac 6 cua bang sau theo thl.P ti,!' gia tri tang d~n.

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8U'&C 1: Tfnh nh~m ho~c lam tren gicfiy nhap d~ tlm cac ket qua a tat ca cac 6.

BU'(yc 2: Sap xep cac k~t qua d6 theo gia tri tang dan.

8U'(yc 3: Di~n so thl.P tl,J' lien tiep theo day so tl,J' nhien vao cac o da dU'Q'C sap xep theo thl.P tl,J' gia tri tang dan, 0 c6 gia tr! nh6 nhat trong bang dU'Q'C danh so 1.

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: Vi d1,1: Em hay sap x~p cac k~t qua, gia tri, ... trong cac o cua bang sau theo ' I

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thu tt,P gia tri tang dan.

t 267t Gia tri nh6 nhat Gia tri nh6 nhat

an- cua ham so 3 cua ham so

f ( x) = 3-.2-sin2 x.cos2 x y = 4sinx + 2cosx 5

• 0 • Nghif;lm cua Gia tri cua bieu thtJic So diem bieu dien nghif;lm

phuang trinh 1 - cos x + cos2x cua phuang trinh

../4x - 9 = 2x - 5 sin2x- sinx sin3x + sin5x = sin4x

v&i cot x = 11 tren du6'ng trcm luqng giac

• 0 0

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