Đề học sinh giỏi huyện Toán 6 năm 2018 - 2019 phòng GDĐT Nậm Nhùn - Lai Châu

PHONG GD&DT NAM NHI]N DE THI CHQN HOC SINH GIOI CAP HUYEN Nim hgc 20t8-2019

DE THI CHiNH THUC (Di thi gim 0ltrans) M6n thi: Torln 6 Ngdy thi: 1310112019 Thoi gian.ldm bdi: 150 phrit (Kh6ng k€ thdi gian phdt d€)

DA bni

CAu 1: (4,0 tli6m). Thuc hi6n phdp tinh

a) 155.155 - 155.41

b)

114

2to .s5 + 210.26

28.27 c) 134- {150:50+ [120: 4+25-(12+ l8)]] d) 100: {2s0: [450-( 4.53 -22.2s)]\

CAu 2: (4,0 tli6m). Tim x, bi5t a) zs<s' <tzs b) 7.7 **1 :343 c) l2x- sl= t3 d) 11- s6 tu nhi6n x lon nh6t sao cho 198 + x vit270 -x ddu chia h6t cho x.

CAu 3: ( 4,0 tli6m). So srinh

a) 1255 vit251

b) 2'm vd 10248

c) 222333 vit333222

d) 32" vd 23'(voi n e N-)

CAu 4: (6,0 tti6m).

Cho doan theng OC = 9cm vd di,5m A nim gi&a 2 di6m O vd C sao cho OA = 6cm.

a) Gpi B Ii trung di€m cria OA, rinh dQ ddi do4n th6ng BC. b) Chtmg t6 rihg A ld trung di6m cta doan thing BC. c) Goi I Ii trung di6m cria doan thing OC. H6i I c6 ld trung di6m cta doan thing AB kh6ng? Vi sao?

CAu5: (2,0tli6m).Tinht6ngd6ys6sau: A= l+ 7 +72 +73 + ...+72,',,,

---------u6t-----_ (Thi sinh kh6ng duoc si'd4ng tdi liQu, Gidm thi coi thi kh6ng giai thich gi theml

U1

h."--

AL-.'

PHONG GD&DT NAM NHUN noc oB ruI cnixn rnrlc xi rur cHeN Hec srNH Gror cAr uuvpN Nim hgc 2018-2019 M6n thi: Torln 6

Ciu Y Hufn g din ch6m Di6m

1 (4,0d)

a

155.155-155.41

l14

155(155 - 41) tt4

155.114

114

= 155

0,5

0,2s

0,25

b

2".55 + 2t0.26

28.27

_2'o(55 + 26) ^8.1

210.81

n8 rl 2.3

210.34 a8 r] ^/. .3

-22.3 -12

0,25

0,25

0,2s

0,25

134- {150 : 50 + [120 :4 + 25 - (12 + 18)]] :r34 -[3 + (30 +25 - 30)] :134 - (3 +25) :t34-28 : 106

0,25 0,25 0,25 0,25

d

100 : {250: [ 450 - ( 4.5'- z'?.25)]\ : 100 : {2s0 : [ 4s0-( 4.t2s - 4.25))] : 100 : {250 : [ 450-( 500- 100)]] : 100: [250: (450-400)]:100: (250:50) =100:5=20

0,25 0,25 o?s 0 ?5

I (4,0d)

25<5'<125

=52 <5* <53

=2<x<3 Do d6 x:2;x:3

0,5

0,25

0,2s

1/3

b

7.7 "*t :343 >'l**2 : 73 )x+ 2:3

= x:1

0,5

0,25

0,25

c

lzx- sl= t: *TH1:2x-5=13 + 2x= 13+5=2x:18+x:9 *TH2:2x-5:-13 +2x:-13+5=2x:-8+x=4 V{y x:9 ;x:4 0,25 o)5

0,25

0,25

d

Tac6(198+x)ix +198i x (270-x)ix+270:x Md x l6n nh6t n€n x le UCLN (198;270) lg8:2.32.11 270 :2.33.5 = tjctN (t98; zto) =2.32 = t8 vOv : 18

0,25

0,25

0,25

0,2s

3 (4,0d)

a

l25s vit257 Ta c6: 1255: 153;s= 515

257 :15217 :5ta Vi15>14+5r5>5ra N6n 1255 > 257

0,2s 0,25 0,25 0,25

b

2t0o vir 10248 Ta c6: 10248: 12r)8: 280 Vi 100 > 80 + ztoo > 280 N6n 2roo > 10248

0,25 0,s 0,25

c

222333 vit333222 Tac6:222333 -(222')"' 333222: (3332)"' Ta sE so sitnh2223 vd,3332 Ta c6 2223 = (2. I 1 l)3 : 23. I 1 13 : 8.1 I l3 = 888. I I l2 3332: (3.1I l)2:32.t l12:9.1112 Vi888>9 =+ 888.1112>g.lll2 =2223 >3332 Do d6 222333 >333222

0,2s

0,25 0,25 0,25

32n vd z3n Ta c6: 32n:132;n= 9n 23n=123yn:gn Vi9>8+9n>8"(VineN-) Nen 32n > 23n

0,25 0,25 0,2s 0,25

2t3

d

4 (6,0d)

a

o BIA C

Vi B ld trung di€m cria OA n6n Oe: !=!=z 22 Ta c6 A nim gifra O vd C, mir B nim gita O vd A vi OB < OA ( 3 < 6), n€n B nim gita O vd C +OB + BC: OC hay 3 +BC:9 +BC:9-3:6(cm)

(cm)

0 5

5

0 5

0 5

0

b

Di€m A nim gita I y16 n6n 661- ag : OC Hay 6 + AC :9 =AC :9 - 6: 3 (cm)

L4i c6: B ld trung diiim crla OA n6n ne : $ = ! =:1cm) 22 =AB: AC:3 (cm) (l) M4t khric B vd C thu6c 2 tia d6i nhau chung g6c A n6n di5m A nim gita hai diiim B vd C (2) Tir (l) vd (2) suy ra A ld trung diiim cria doan thing BC.

0

0

5

5

0,5 0,5

Vi I ld trung di6m cria do4n thing OC n6n I nim gita O vd C, md A vd B thuQc 2 tia d6i nhau chung g5c I n€n di6m I nim gita hai <Ii6m A vd B n6n:

oB + BI :or: +=?=a,s(cm) 22 Hay 3 + BI : 4,5+BI -- 4,5 -3 : 1,5 (cm) Tuong tg ta c6 IA: 1,5 (cm) + IA: IB :1,5 (cm), mir I nim"giira hai tti6m A vi B. Vdy I ld trung di6m cria doan thing AB.

0

0

0

5

5

5

0,5

5 (2,0d)

NhAn c6 2 v6 cria A vdi 7 ta duoc: 7A:7(l +7 +72 +73 + ...+72ooi) :e +72 + 73 +...+ 72008) Md A: 1+7 +72 +73 + ...+72'n7 NCnTA-A=6A. -72008 -l -2008 VAvA: t -l

6

0

0 5

5

05

o5

J/ J