Đề thi HSG Toán MTCT lớp 12 Thái Nguyên 2013-2014 vòng 1 - Học Toàn Tập

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UBND TINH rHAr

xcuvpx

sO

cmo

DUC & DAo

r4o

Bt,

cniNs

rHtlc

KV

rHr

cHeN

Hec

sINH

GI6I

cAr riNH

GrAr

roAN

rnBx

MAY

riNu

cASIo

LaP

D

NAU

Hoc

2an-2014

Thoi gian:120 phrit (Kh6ng tee

*at

gian giao

di)

Ngny thi:15110/2013.

Chri:f :

l,

Thi ,sinh duqc sw dqng m$t trong cdc

loqi

mdy t[nh sau: Casio fx-5A0A,{5, ES;
CasiaJx-57AMS, ES PLUS; C*sio.fx-500 yNPLUS; Vinacal Vq-SAAMS, 570M5 vd Vinacal-S71M| New.
2, Ndtt kkdng ndi gi th\ru hdy tfrch ckinh xdc ddn

I

chil'sA ,sau ctfru phiiy.

3, DA thi gdm cd

04

trang

4, Thi sinh ldm bdi tn1'c ti€p vdo

di

thi nfu,,

Di€rn bAi thi Girim kh6o I Gi6m kh6o 2 Sd phdch

B[ne s6 BIng

cht

Bei

1(5 dihm):

Cho d6y s5 2, 6, 30, 210,

...

dugc x6c dinh nhu sau: 56 hang th:ir

k

bdng tich cira

(

s6 nguy6n tO dAu ti6n (k

:

1

,2,3,...).

niet

ring

c6 hai sO hang cua d6y c6 hiQu

b6ng 30000.

Tim

hai s0 tl6.

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Bni

26

iriam):Khai

tri6n nhi

thric

(ry*g''

_l'*

dusc mQt da thrlc (bii5n

r).

Tinh

I12

zal.3)

tting c6c hQ sO cira da thrlc tl6.

So laqc cdch gidi: t qua:

Bni 3(:i ttidm): Cho d5y _{sO 1U,,1}x6c dinh nhu

sau:

U,

:

tr,

U,

*

l

I

Un+:

:

2U,+r

_-

tU, *

4,

(Vn

€ N*,n

l

1).

a) H6y 10p quy

trinh

1i0n tpc bAm phirn

tim

cdc sii hpng cua ddy sO dO.

b)

Tirn

U,r; U,r;

U,o;

[J,,

<iuoi dpng ph6n sO

t6i

gian.

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Bni

4(i

itivm):cho

phuong

trinh

,tr. ffi

=

o (r)

a) ViSt mQt quy trinh b6m phfm gi6i phuong

trinh

(t)

va cho bii5t k6t

qui

.

b) Chung minh

ring

nghi$m

tim

dugc o phAn a) ld duy nh6t.

So fuqc cdch

gidi:

KAt qud:

Bht

5(

;BC.A'B'C'c6

<i6y

ABC.li

tam gi6c vuong

tqi

B,

AB

_-2,L3;

,$/)

_-

4,26;

A'C

_=6,39

.

Gqi

M

ld

trung di€m

cria dopn thdng

A'C',,M

li

giao

di6m

ct.r.

AM

vd

A'C.

Tinh

th€ tich

tnOi

ttr

dien

N,4BC

vi

khof,ng

c*ch tir

A

d}nmdt phin _s,(NBC).

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Bni

6(5

iti6@:

Tinh gAn dring gi6

trf

lon nh6t

vd

gi|tri

nh6 nh6t cria

him

s6:

2.x2-8x+1

Jlx)=-

2,

-

^--l -r^-rL

So luqc cdclt gidi: t qua:

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