đề thi máy tính bỏ túi lớp 9

đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9đề thi máy tính bỏ túi lớp 9v

Bg GIAo DUC vA o,4.o r+g

DE TrU CrfiruIl TITIIC

cugc rnr cr*& roANrnnx mAy rlrvn cAu ray

Nau zora

M6n ToSn Lop 9 CAp THCS Thoi gian thi: 90 phtttghbng ru *rAf gian giao dA)

Ngdy thi : ti\tzOru

c.!( i: - ai m gam 6 tuang, 5 bdi, n di bdt 10 dient Thi sinh ldnt bdi nqc riep vdo bdn

de tlTt nay,'

t\/€u de bai kitSttg co y?u cdu ri€ng tlti k€t qzid ldni *-dn din 4 ch* si thip phdn. Bli 1" (10 di6ni)

Cdu 1 (a di6m) Tinh giatricria bi6u thirc sau:

n _ l, z, 3, too4z 1005, 1006, 1.3 3.5 5.7 ""' 2007.2009'

200g.n11- 201L20r3.

cf,u 2 (6 dicm) cho dathirc p(x) :6x4

-7x3 -12x2* ax * 2 vd e(x) :x, +bx-Z.

a) xilc dlnh a, b {daoi dqtng sd nguy€n hofic phdnsa; ac da thfic p(x) chia hiit

b) vdi a tim ducvc hdy tim tat chc6c nghiQm cria da thric p(x).

DIEM CUA TOAN BAI THI C6c gi6m khdo

(Hg, t€n vd chf k0

SO PHACH

(Do Chn tich HOi d6ng thi khu wc ghi)

Bing sd B5.ng chfr

r*;=*'

F r"r t 1',T r

i i ur:'* i-q: *

t* *****

*-"t t -srr*et,'ii'E i

f'; i ibl i*r ii _f 1 r ,i.J'u,r n

!

Trinh bAy r6m 'tgt cech

giAi vdo phAn dudi d6y.

Ciu 1.

,.

KCt qufr :

Cfiu 2,

Bei 2 (10 dicm)

e4u i 1s dicni) Trdn,hai i4nh'BC, AC cria tam giacddu ABC, lAy tucrng img hai diQ M,vg N sao'cho BM :'C\, Tim vi tri cfi-alr11 dC dO ddi dopn thang IvIIrl co giit

tri nhd nnAL Tfnh gi:i tri nh6 nh6t cria MN, bi6t dA ddi canh cria tam gi6c d6u ABC

ld Jno:zotq cm

cau 2 (5 diem) MOt l&oi 96 rrintr lap phuong canh x (cm) o chfnh gina m6i m6t

cria h]nh l0p phucnrg, nguoi ta dpc mQt I5 hrn! vrr6ng thdng sang m{t diii dign, te*

cria 16 hinh vudng ld t6m cria mflt hinh lflp phucrng, c6c canh 16 hinh vu6ng song song v6:i c4qh cfia hinh lflp phuqng (nhu hinh yQ Timthe tfch V vA t6ng diQn tich

s c6c mgt (ngodi vd trong) theo x vd y cria kaoi g5 sau khi duc xong Ap dung v6i

x -56,7'' cm;r y =1 1,4cm.

2

Trinh bdy t6m tlt cdchgiAi vdo phAn du6i d6y.

Cf;u X".

KCt qui :

K6t ouf,:

| 2 L.

Bei 3 (10 di€m) Cho day s6t xr= xr= 1;r: = 2,x,*= x,*z-1x,*t***,, v6'in : 1,2,3,

5l

Vi0t quy trinh bdm rn6y tinh x,., r6i sft dpng quy trinh d6 tinh x15,x2s7x25.

tom t|t circh dn dusi dd

tsii 4 (10 diem) Cho tam gi6c ABC vudng tqi.A.6 AF ld dudng cao vi BH:

4cm, CH : 9cm Gqi D vd F l6n luqt la hinh chi6u cira di6m H tr0n AB vd AC Gqi

M vA N iAn iuqt ld trung di6m cria BH vd HC Gqi O ld tdm vd R ld bdn kinh cira duong trdn nQi ti0p tam gi6c ABC .HIy tinh :

Cdu 1 (2 diem) E0 dei DE?

Cf,u 2 (2 digm) Cliu vi tam gi6s 4FC?

Cdu 3 (Z AiCm; SO do (ldm trdn den phrit) g6c.ABC vd goc ACB?

CSu 5 (2 diem) B6n kinh R?

Trinh bdy t6m tht cdchgidi vdo phan auOi Oay.

4

Bili 5 (10 diem)

Anh A mua nhd tri gi6300000000 cl6ng (ba trdm triQu d6ng) theo phucrng

thrlc trh g6p.

Cflu 1 (5 die@ NOu cu6i m6i th6ng bdt d6u tu thrlng thf nhat anh A trA

5.500.000 chiu 15i xudt sO ti6n chua trd ld 0,5%olth6ng thi sao bao 16u anh Atrh

tr6t s5 ti6n trOn.

Ciu2 (5 di6m) Ni5u anh A mudn trih€tng trong vdng 5 ndm vdphhitrh

ldi v6i mitc |ohlndm thi m6i th6ng anh A phhi trdbao nhi6u ti6n (ldm trdn dtin

nghin d6ng)

Trinh bdy t6m tht cilch gi6i vdo phAn du6i c16y

K6t quf,:

Ciru 2.

KGt qui:

Bq GrAO DrJC VA DAO TAO CUQC TI{I GIAI TOANTRf,N MAY TTNH CAM TAY

NAM 2014 M6n Toin LW 9

I{UdNG DAN GI,dI IIOAC NAP SO

CAp TIICS

Bhi L (10 ditlm)

CAu 1 (a diem) Tinh gi5 tri cria bi6u thric sau:

12 2' 3' ioo4'z 1005'z 10062

,l-

-+ - +

+ +-* -:-: * -: -: -1.3 ' 3.5 5"1 2007.2009 2A09.2011 2all-20r3 c6u 2 (6 dicm) cho da thirc P(x) : 6* *7f - 12* * ax * 2 ve Q(x) : x' + bx-2'

a) x1cdinh a, b (daoi dqng s6 nguyan hofic phdn"a; ac da thirc P(x) chia h6t cho Q(x)

b) Vdi a tim dugc hdy tim tdt chc6c nghiQm cira da thric P(x).

Ciu 1.

r =- -T- T

T-T-'^ - 1.3 ' 3.5 ' 5.7 "" ' 2\A7.2AA9 '

2009.2011 2011.2013

t( t' f 22 z' 32 32 10052 10052 10062 1006'? )

=-l

r[t', ( z' -1'), f 3' -2'\,, (t00s'-10042) (tooo'-toos']-Uq(l

=ilr.[ , J.[ , J* *[ 2ooe J.[ zorr f ,* )

rl

l,

=ll , n(zott-z *r)_tooe' l-sooszt =z5r.6z4s3is

l\-l

l- rdng cric sdi l

K6t qun t A 251,6249 Cf,u 2.

a)Tac6P(x):Q(x).(6x2 ' (7 +6b)x+ 7b+6b21+ (a- 6b3 -7bz -lzb-14)x + 12bz +

14b+2

ocr1xl i Q(x) <+(a-6b3- l*-na-14)x +labz + 14b *2:0v6i Vx

[a - 6b3 -7b2 -tzb-14 = o(i)

el-[tzu'+14b+z=0(2)

GiAi phucrng trinh (2) tadugc hai nghiQm b : - 1 'rra b = -l .

6 l^-73 Thay b:- 1 vd b=-+vio (1) a,rq I ?=t,ho+c ]*- 6

L" o

(^ -c lu=T

K6t qu6: ll -' ; ]

lb=-l'l, 1

Lb

+ Vdi a:3 c6 P(x) : 6xa -l* - tz* + 3x+ 2

Giii phucrng trinh duoc

KrSt qu6: xr:2)x2: - t; or:l '2 : 0,5; *: -l 3 = -0,3333

-4 l1

+ V6i u: a co P(x) :6x4 -7x3 - 12x2 + !x+ 2

6"5

GiAi phucrng trinh dugc

R.,L?

K6t qu6: x1:1,1455; ve: -0,1455; n, :-i = -1,3333,xq:1 =7,5

Bei 2 (10 dicm)

C6u 1 (5 di€m) Tr€n hai canh BC, AC cria tam gi6c dOu ABC, lAy,tuong tmg hai di€m M vd N sao cho BM : CN Tim vi tri cria M de dO ddi doan thlng MN c6 gi6

tri nh6 ntrAt finn gi6 tri nhO nhat cta MN, bi6t canh cta tam gi6c dAu ABC ld

Jzaolzou cm"

Cffu 2 (5 diCm) Mqt kh6i 96 hhh lpp phucmg c?nh x (cm) O chinh gita m6i m6t

cria hinh lflp phuong, ngudi ta dpc m6t 16 hinh vu6ng th6ng sang mflt d6i diQn, tam cria l5 hinh vu6ng ld t6m cria m{t hinh lflp phucrng, c6c c4nh 15 hinh vu6ng song song v6i cpnh cria hinh lQp phucrng (nha hinh yd) Tlm th6 tich V vd t6ng diQn tich

S c6c mgt (ngodi vd trong) theo x vd y cria tctrOi 96 sau khi dpc xong Ap dung vdi

x:56,'7 cm, y:11,4cm.

c

CduL.Ke MKLAB ( K AB);NH LAB (HeAB )vd MGINH (GeNH).

Tir gi6c MGHK la hinh cht nhflt vi c6 ba g6c vudng

+ MG=KHmd MN>MG =) MN>KH

CSctamgi6c AHN, BKM d€u ld tam gi6c vu6ng c6 mQt g6c nhgn bing 60o

=+ AH=N 22 ;BK=BM

'2 2u : AB-AN + NC

= AB- AC 22 - AB

Suy ra: * ,4 2,, \ / , min (,aDl) = S 2 o MN Lilducrng trung binh cria AABC

* IvrN:AB 22-JitrC82o14 =2237.856899

K6t qu6: MN: 2237,8569 cm

2

BM

C6u 2.

v: x3 - o.[]J)r'-r'

\2 )"

Di0n tich 6 m4t ngodi lit:6(x2 -f}

Diqn tich c6c m6t trong ldL: 6.[(x-y) :2.y.4]

Vay diqn tich c6c mflt 16 :,S = 6(x' - y')*t -[?r)

v=153 14i,155 cm3 S= 24 706,62 cmz

th6 ticfr hinh c6n tinh bdng the tich ttr6i t6p phuong ban dAu ffi di th0 tich 6 kh6i hinh hQp chft nhat d6y ld hinh w6ng .ait y cm, chidu

"uo fa 1x-yi:Z; rOi tru di

thd tich ttr6i t6p phucrng canh

y cm.

Bni 3 (10 diem) Cho ddy s6: ,, = x2=l;xr=Z)x,*z=**r-1**r*f,.*,, vdi n : 1,2,3,"'

Vi€t quy trinh b6m m6y tinh xn r6i sir dpng quy trinh d6 tinh x151x2s,xs5.

Thuc hi€n tr€n m6v fx-570MS:

@E H 3@ EE i@ E@@E (duqc xa)

@ " E ;@EE ;@E@ @E (dusc x5)

@E H ?@EE ;E@E ffi mE (duqc x6)

ffi@E(duqcxz)

@@E(ctuscxr)

ffi"fiffiip ddu bing, trdn mdn hinh m6y tinh xu6t hiQn:

I 109

*u =ffi, x?o = 0.1978507786 , xzs = 0'1060976856 '

- K5t quf,: xr: =0,5705 , x?o=0,1979, xzs=0,1061' '\

BAi 4 (10 diCm) Cho tam gi6c ABC ru6ng tpi A c6 AlI ld ducrng cao vd BH :

4cm, CH: 9cm Gqi D va p lAn luqt ld hinh chi0u cria di0m H trOn AB vi AC Gqi

M vd N lAn luqt ld trung di6m cria BH vd HC Gqi O ld t6m vd R ld b6n kinh ctra

dudng trdn nQi ti6p mm gi6c ABC HAy tinh :

CAu 1 (2 di0m) D9 ddi DE?

Ciu2 (2 di€m) Chu vi tam giSc 4PC?

Ciu 3 (2 di0m) SO <1o (ldm trdn d6n phft) g6c ABC vd g6c ACB?

Cf,u 4 (2 di6m) DiEn tich tfr gi6c EDMN?

CAu 5 (2 diem) B6n kinh R?

1) Ta c6 DE: A}I : JEIt.cH : 6 cn'r

Z!)Tac6 AB : .[7H\ 811' = JT6 +16 =ZJB cm Tucrng t.u ta c6 4! : :Jtl cm. Mdi kh6c BC: BH + CH: 13cm V?y chu vi tam gi6c ABC : 5fi3 +13 :

31,0277 5638

KGt qui: 31,0278 cm 3) Ta c6 sinc:g='^l\'-*7ea *3304t, >m *56otg'

a) Gqi I ld giao di6m cria AH vd DE

iu

"i i6fr-=1frD vit ffiH =frH-D MAt l&6c friD+1fii=e00 = ffiH *i6E =eoo (1)

Tuong Ts ta c6 fEE +frEE =eOo(2) Tt (1) vn (2) suy ra MD/NE (vi MD vdNE cirng vu6ng g6c v6i DE) suy ra tu gi6c EDMN 1A hinh thang ur6ng

0 - (MD*!E)pL

-(2+!,5)6 =19,5

= )pDtvfN- Z - 2 ,

K6t qu6: L9,5 cnf

5) Ta c6 s*r" : s aonu * s oon"* sorr o

lea.dc =|er.n*L,qc.n*! nc.a

78

eR=2,513878i89cm

zJtz +3fi + 13

:2,5139 cm

Bei 5 (10 di6m) Anh A mua nhd tri gi5 300000000d (Ba trdm triQu d6ng) theo

phuong thirc tr6 g6p

ba* f 1S diem) Neu rrOi m6i thang Uat OAu dr thang thri nhat anh A tra 5500000d vd

chiu ldi xo6t sO tiAn chua tr6 ld O,So/olthang thi sau bao lAu anh A tra h€t s6 ti0n tr0n'

Cdu 2.(5 diem) Nt5u anh A mu5n tr6 h6t ng trong vdng 5 ndm vd phAi tra.lei v6i mric

|o/olndmthi mdi thang anh A ph6i t6 bao nhiOu tidn (dm trdn d6n nghin d6ng).

uau .{

Cqira ti6n anh A nq ban dAu le M, 15i xu6t anh ta phii tr6 lit ro/olth6ng, s6 tiAn hdng th6ng anh ta ph6i tri ld x

- CuOi th6ng thir nh6t anh A ng ld: u +! u = M(r* *) = ptt,

Anh A ddtrbx dtrng, vay sO tiOn cdn ng ld: Mk-x

- CuOi th6ng thir hai anh A ng ld: (Mk-x)k* x= Mkz-x(k+ I) = Mk' -.+:] k-1

1

o )zJG:Ji5 = (Jtl +

K6t qun

A

+

- Sau n th6ng anh A trA xong ng, nghia ld Mn: 0 hay:

- CuOi thdngthir 3 anh A cdn ng lit: (Mk'?-*t:))t -x=Mk'-.#

- CuOi th6ng thir n anh A ng ld:

M - = ( Mk,'r - *k"-' -l\k - x : Mkn - o: -l = k, (M-

=il +- rr- = (t * *)' (u -100* )* I 00x

"n \- - k-l ' k-l k-l' k-l 100' r r

r - 100r (1+-)" =+ ' 100' lj\x-Mr

Duns Mrcr voi M: 3000000ttlir;lf;l;fl?:100, ta dusc n :64 .

l\!L tlu4' vr Lrrqrr6'

C6u 2 Goi sO ti€n anh A ng ban ddu la M, ldi xu6t anh A ph6i tr6 lir roZlndm, s6

tidn hAng inarg anh A phiitrilld m, Mnld sO tiAn cdn no sau n ndm Ta c6:

Mt:M(t+r%)-t2rn

tuir: I i,t(l + r%o) - I 2 mJ ( +r%o) - I 2 m: M ( ] + r%o)2 - I 2 m ( t +r%+ I )

(l+ rYo\z -l

: M( I +r%r)2 - 1 2y : =t

-ro/o

,t\2-r )*(r+r%)z -l *rrrs-rr*(l+ rYo)t -l

M3: I M( 1 + r%o)' - I 2 7n : ":- J Q + r%o) - I 2 m : M ( ]

n + ryo), _l

-,:

M(]+r%o)"-12m\' ;;

rYo

Ap dung v6i M:300.000.000; r:6; n: 5 vi M5:0 ta dugc:

0:300000000 1,065- n*r'0! ): 1

0,06

1 06'.30rye0009.04q:

s9349 1 0.01 r SuY ra: m: -' :I

:

r '*''-'

- (1,06' -l)'12

K6t quf,: 5935000 ddng

tsg GIAO DUC vA DAo r'4o cuQC THI GrAx roAN TREN MAy riNH caRr uav

nAna zor+

h,{6n To6n LW 9 Cap THCS

Bap Aiv vA rnaruG DrEM

(10 diem)

(10 di6m)

Kct qu6: xrs = 0,5105 , xro =0,1979 , xzs = 0,106i

Bni 4 (10 di6m)

CAU 1 K€t qu6: 6 cm

Cdu 2 KOt qui: 31,A278 cm

Cffu 3" ldB =3304r',78e = 56019'

Ciu 4 K6t qu6: 19,5 cmz

Cfiu 5 K6t qu6 :2,5139 cm

M6iy2

di0m

Bni 5.Ii0 (i0 di6m di0m)

Cffu 1 KOt qui

Cf,u 2 KOt qu6

64 thang.

5 934 910,011 d6ne

5 diOm

- -.4

) olem

Chrt ! : T6 chtim thi cdn cu vdo hadng ddn gidi d€ chia diAm.chi fidt Cdc cdch giai khdc ndu dilng, gidm khao cdn c*vdo khuig thaig di\m de cho drcm.

Eai 1" (10 diem)

Ciu 1 KCIt qu6 :

C,du2.Kt5t qu6:

Ul K<it qu6: x1 :

A = 251,6249

l^ _tE (^

u)lu=r ' l.b:-1'lr_ '] 6I

tu -l.6

2; xz:- 1; x: : 1 : 0,5; xa : -1 = -0,3333

23

455;x2:-0,I455: 4 1^'^^ 3

":-J = -t'5 J55t*:,

4 di6m

6 di6m

Rii 2 (10

Cffu 1 KOt qu6

CAu2.Ki5t qui

MN : 2237,8569 cm

V=l53 141,155 cm3 S:24 706,62 cmz

5 di6m Rii 3 (10 di6m