bo 54 de thi vao thpt nam hoc2011-2012 mon toan

B THI VO THPT CA 54 TNH NM HC 2011 - 2012

SU TM: ON TIN TRUNG - Ph hiu trng THCS Hong Vn Th - N 1

S GIO DC V O TO

PH YN

---------------------------

K THI TUYN SINH LP 10 THPT

NM HC 2011 2012 Mn thi : TON

Thi gian lm bi : 120 pht, khng k thi gian giao Ngy thi : 27 thng 6 nm 2011 ( bui chiu)

Cu 1 (1.5 im) Rt gn cc biu thc sau:

1 1

3 2 2 3 2 2 ;3 1 3 1

A B

Cu 2 (1.5 im) 1) Gii cc phng trnh:

a. 2x2 + 5x 3 = 0

b. x4 - 2x

2 8 = 0

Cu 3 ( 1.5 im) Cho phng trnh: x2 +(2m + 1)x n + 3 = 0 (m, n l tham s)

a) Xc nh m, n phng trnh c hai nghim -3 v -2. b) Trong trng hp m = 2, tm s nguyn dng n b nht phng trnh cho c

nghim dng.

Cu 3 ( 2.0 im) Hng ng phong tro thi uaXy dng trng hc thn thin, hc sinh t ch cc, lp

9A trng THCS Hoa Hng d nh trng 300 cy xanh. n ngy lao ng, c 5 bn c Lin i triu tp tham gia chin dch an ton giao thng nn mi bn cn li phi trng thm 2 cy mi m bo k hoch t ra. Hi lp 9A c bao nhiu hc sinh.

Cu4 ( 3,5 im) Cho hai ng trn (O) v (O) c cng bn k nh R ct nhau ti hai im A, B sao cho

tm O nm trn ng trn (O) v tm O nm trn ng trn (O). ng ni tm OO ct AB ti H, ct ng trn (O) ti giao im th hai l C. Gi F l im i xng ca B qua O

.

a) Chng minh rng AC l tip tuyn ca (O), v AC vung gc BF. b) Trn cnh AC ly im D sao cho AD = AF. Qua D k ng thng vung gc vi

OC ct OC ti K, Ct AF ti G. Gi E l giao im ca AC v BF. Chng minh cc t gic AHOE, ADKO l cc t gic ni tip.

c) T gic AHKG l hnh g? V sao. d) T nh din t ch phn chung ca hnh (O) v hnh trn (O) theo bn knh R.

THI CHNH THC

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uBND tinh bc ninh

S gio dc v o to

thi tuyn sinh vo lp 10 thpt

Nm hc 2011 - 2012

Mn thi: Ton

Thi gian: 120 pht (Khng k thi gian giao )

Ngy thi: 09 - 07 - 2011

Bi 1(1,5 im)

a)So snh : 3 5 v 4 3

b)Rt gn biu thc: 3 5 3 5

3 5 3 5A

Bi 2 (2,0 im)

Cho h ph-ng trnh: 2 5 1

2 2

x y m

x y

( m l tham s)

a)Gii h ph-ng trnh vi m = 1 b)Tm m h c nghim (x;y) tha mn : x2 2y2 = 1.

Bi 3 (2,0 im) Gi bi ton bng cch lp ph-ng trnh hoc h ph-ng trnh:

Mt ng-i i xe p t A n B cch nhau 24 km.Khi i t B tr v A ng-i tng thm vn tc 4km/h so vi lc i, v vy thi gian v t hn thi gian i 30 pht.Tnh vn tc xe p khi i t A n B . Bi 4 (3,5 im)

Cho -ng trn (O;R), dy BC c nh (BC < 2R) v im A di ng trn cung ln BC sao cho tam gic ABC c ba gc nhn. Cc -ng cao BD v CE ca tam gic ABC ct nhau H.

a)Chng minh rng t gic ADHE ni tip .

b)Gi s 060BAC , hy tnh khong cch t tm O n cnh BC theo R. c)Chng minh rng -ng thng k qua A v vung gc vi DE lun i qua mt im

c nh.

d) Phn gic gc ABD ct CE ti M, ct AC ti P. Phn gic gc ACE ct BD ti N, ct AB ti Q. T gic MNPQ l hnh g? Ti sao?

Bi 5 (1,0 im)

Cho biu thc: P = 2 2( 2)( 6) 12 24 3 18 36.xy x y x x y y Chng minh P lun

d-ng vi mi gi tr x;y R

chnh thc


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S GIO DC V O TO K THI TUYN SINH VO LP 10 THPT TNH B RA VNG TU Nm hc 2011 2012 ------------------- ----------------------- CHNH THC Mn thi: TON Ngy thi 08 thng 07 nm 2012 Thi gian lm bi : 120 pht ( khng k thi gian giao ) Bi 1: ( 3,0 im) a) Rt gn: A = 3:)327212(

b) Gii phng trnh : x2 - 4x + 3 =0

c) Gii h phng trnh:

1

42

yx

yx

Bi 2: ( 1,5 im) Cho Parabol (P): y = x2 v ng thng (d) : y = 2x + a

a\ V Parabol (P) b\ Tm tt c cc gi tr ca a ng thng (d) v parabol (P) khng c im chung

Bi 3: ( 1,5 im): Hai t cng lc khi hnh t thnh ph A n thnh ph B cch nhau 100 km vi vn tc khng i.Vn tc t th hai ln hn vn tc t th nht 10km/h nn t th hai n B trc t th nht 30 pht.Tnh vn tc ca mi t trn. Bi 4: ( 3,5 im) Trn ng trn (O,R) cho trc,v dy cung AB c nh khng di qua O.im M bt k trn tia BA sao cho M nm ngoi ng trn (O,R).t M k hai tip tuyn MC v MD vi ng trn (O,R) (C,D l hai tip im)

a\ Chng minh t gic OCMD ni tip. b\ Chng minh MC2 = MA.MB c\ Gi H l trung dim on AB , F l giao im ca CD v OH. Chng minh F l im c nh khi M thay i

Bi 5: ( 0,5 im) Cho a v b l hai s tha mn ng thc: a2 + b2 + 3ab -8a - 8b - 2 ab3 +19 = 0

Lp phng trnh bc hai c hai nghim a v b


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S GIO DC V O TO K THI TUYN SINH VO LP 10 TRUNG HC PH THNG

K LK NM HC: 2011 2012

THI CHNH THC Mn thi: Ton Thi gian lm bi: 120 pht, khng k thi gian giao Cu 1. (2,0 im)

1) Gii cc phng trnh sau: a/ 9x

2 + 3x 2 = 0.

b/ x4 + 7x

2 18 = 0.

2) Vi gi tr no no ca m th th ca hai hm s y = 12x + (7 m) v y = 2x + (3 + m) ct nhau ti mt im trn trc tung?

Cu 2. (2,0 im)

1) Rt gn biu thc: 2 1

.1 2 3 2 2

A

2) Cho biu thc: 1 1 1 2

1 . ; 0, 111 1

B x xxx x x

a) Rt gn biu thc B. b) Tm gi ca ca x biu thc B = 3.

Cu 3.(1,5 im)

Cho h phng trnh: 2 1

(1)2 2

y x m

x y m

1) Gii h phng trnh (1) khi m =1. 2) Tm gi tr ca m h phng trnh (1) c nghim (x ; y) sao cho biu thc P = x

2 + y

2 t gi tr nh nht.

Cu 4.(3,5 im) Cho tam gic ABC c ba gc nhn ni tip ng trn (O). Hai ng cao BD v CE ca tam gic ABC ct nhau ti im H. ng thng BD ct ng trn (O) ti im P; ng thng CE ct ng trn (O) ti im th hai Q. Chng minh rng:

1) BEDC l t gic ni tip. 2) HQ.HC = HP.HB 3) ng thng DE song song vi ng thng PQ. 4) ng thng OA l ng trung trc ca on thng P.

Cu 5. (1,0 im) Cho x, y, z l ba s thc ty . Chng minh: x2 + y2 + z2 yz 4x 3y -7.


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S GIO DC V O TO K THI TUYN SINH VO LP 10 THPT

KIN GIANG NM HC 2011 2012 CHNH THC MN THI: TON ( thi c 01 trang) Thi gian: 120 pht (khng k thi gian giao ) Ngy thi: 22/06/2011

Cu 1: (1,5 im)

a) Tnh: 12 75 48

b) T nh gi tr biu thc 10 3 11 3 11 10A Cu 2: (1,5 im)

Cho hm s y = (2 m)x m + 3 (1) a) V th (d) ca hm s khi m = 1 b) Tm gi tr ca m th hm s (1) ng bin

Cu 3: (1 im)

Gii h phng trnh : 2 5

3 1

x y

x y

Cu 4: (2,5 im) a) Phng trnh x2 x 3 = 0 c 2 nghim x1, x2. T nh gi tr: X = x1

3x2 + x2

3x1 + 21

b) Mt phng hp d nh c 120 ngi d hp, nhng khi hp c 160 ngi tham d nn phi k thm 2 dy gh,mi dy phi k thm mt gh na th va . T nh s dy gh d nh lc u. Bit rng s dy gh lc u trong phng nhiu hn 20 dy gh v s gh trn mi dy l bng nhau.

Cu 5: (1 im) Cho tam gic ABC vung ti A, ng cao AH. T nh chu vi tam gic ABC bit:

AC = 5cm. HC = 25

13cm.

Cu 6: (2,5 im) Cho na ng trn tm O ng k nh AB; V tip tuyn Ax, By vi ng trn tm O. Ly E trn na ng trn, qua E v tip tuyn vi ng trn ct Ax ti D ct By ti C. a) Chng minh: OADE ni tip c ng trn. b) Ni AC ct BD ti F. Chng minh: EF song song vi AD.


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S GIO DC V O TO TNH NINH BNH

CHNH THC

THI TUYN SINH LP 10 THPT NM HC 2011 - 2012

Mn : TON

Thi gian lm bi 120 pht (khng k thi gian giao )

Cu 1 (2,0 im): 1. Rt gn cc biu thc

a) A 2 8 b) a bB + . a b - b aab-b ab-a

vi 0, 0,a b a b

2. Gii h phng trnh sau: 2x + y = 9

x - y = 24

Cu 2 (3,0 im):

1. Cho phng trnh 2 2x - 2m - (m + 4) = 0 (1), trong m l tham s.

a) Chng minh vi mi m phng trnh (1) lun c 2 nghim phn bit:

b) Gi x1, x2 l hai nghim ca phng trnh (1). Tm m 2 2

1 2x + x 20 .

2. Cho hm s: y = mx + 1 (1), trong m l tham s. a) Tm m th hm s (1) i qua im A (1;4). Vi gi tr m va tm c, hm s (1)

ng bin hay nghch bin trn R? b) Tm m th hm s (1) song song vi ng thng (d) c phng trnh:

x + y + 3 = 0

Cu 3 (1,5 im): Mt ngi i xe p t a im A n a im B di 30 km. Khi i ngc tr li t B v

A ngi tng vn tc thm 3 (km/h) nn thi gia v t hn thi gian i l 30 pht. T nh vn tc ca ngi i xe p lc i t A n B.

Cu 4 (2,5 im): Cho ng trn tm O, bn k nh R. T im A bn ngoi ng trn, k 2 tip tuyn AB,

AC vi ng trn (B, C l cc tip im). T B, k ng thng song song vi AC ct ng trn ti D (D khc B). Ni AD ct ng trn (O) ti im th hai l K. Ni BK ct AC ti I.

1. Chng minh t gic ABOC ni tip ng trn. 2. Chng minh rng : IC2 = IK.IB.

3. Cho 0BAC 60 chng minh ba im A, O, D thng hng.

Cu 5 (1,0 im):

Cho ba s x, y, z tha mn x, y, z 1:3

x + y + z 3

. Chng minh rng: 2 2 2x + y + z 11


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K THI TUYN SINH VO LP 10 TRUNG HC PH THNG

BNH NH KHA NGY :29/06/2011 chnh thc Mn thi: Ton Thi gian : 120 pht ( Khng k thi gian pht ) Ngy thi: 30/6/2011

Bi 1 (2im)

a) Gii h phng trnh : 3 7

2 8

x y

x y

b) Cho hm s y = ax + b.Tm a v b bit rng th ca hm s cho song song vi ng thng y = -2x +3 v i qua im M( 2;5)

Bi 2: (2im)

Cho phng trnh 2 2( 1) 4 0x m x m (m l tham s)

a)Gii phng trnh khi m = -5 b)Chng minh rng phng trnh lun c hai nghim phn bit vi mi m c)Tm m sao cho phng trnh cho c hai nghim x1, x2 tha mn h thc

2 2

1 2 1 23 0x x x x

Bi 3 : (2im) Mt mnh t hnh ch nht c chiu di hn chiu rng 6m v bnh phng di ng cho gp 5 ln chu vi.T nh din t ch hnh ch nht Bi 4: (3im) Cho ng trn tm O, v dy cung BC khng i qua tm.Trn tia i ca tia BC ly im M bt k.ng thng i qua M ct ng (O) ln lt ti hai im N v P (N nm gia M v P) sao cho O nm bn trong gc PMC. Trn cung nh NP ly im A sao cho cung AN bng cung AP.Hai dy cung AB,AC ct NP ln lt ti D v E. a)Chng minh t gic BDEC ni tip. b) Chng minh : MB.MC = MN.MP

c) Bn k nh OA ct NP ti K. Chng minh: 2 .MK MB MC

Bi 5 (1im)

Tm gi tr nh nht ca biu thc: 2

2

2 2011x xA

x

(vi x 0


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S GIO DC V O TO

HI DNG

K THI TUYN SINH LP 10 THPT NM HC 2011 2012

Mn thi: TON

Thi gian lm bi: 120 pht (khng k thi gian giao ) Ngy thi: 30 thng 06 nm 2011

thi gm: 01 trang

Cu 1 (2,5 im).

1) Cho hm s 2( ) 2 5y f x x x .

a. Tnh ( )f x khi: 0; 3x x .

b. Tm x bit: ( ) 5; ( ) 2f x f x .

2) Gii bt phng trnh: 3( 4) 6x x

Cu 2 (2,5 im).

1) Cho hm s bc nht 2 3y m x m (d) a. Tm m hm s ng bin. b. Tm m th hm s (d) song song vi th hm s 2 3y x .

2) Cho h phng trnh 3 2

2 5

x y m

x y

Tm gi tr ca m h c nghim ;x y sao cho 2 5

41

x y

y

.

Cu 3 (1,0 im). Hai ngi th qut sn mt ngi nh. Nu h cng lm trong 6 ngy th xong cng

vic. Hai ngi lm cng nhau trong 3 ngy th ngi th nht c chuyn i lm cng vic khc, ngi th hai lm mt mnh trong 4,5 ngy (bn ngy ri) na th hon thnh cng vic. Hi nu lm ring th mi ngi hon thnh cng vic trong bao lu.

Cu 4 (3,0 im). Cho ng trn (O; R) c hai ng k nh AB v CD vung gc vi nhau. Trn on thng AO ly im M (M khc A v O). Tia CM ct ng trn (O; R) ti im th hai l N. K tip tuyn vi ng trn (O; R) ti N. Tip tuyn ny ct ng thng vung gc vi AB ti M P.

1) Chng minh: OMNP l t gic ni tip. 2) Chng minh: CN // OP.

3) Khi 1

AM AO3

. T nh bn k nh ca ng trn ngoi tip tam gic OMN theo R.

Cu 5 (1,0 im). Cho ba s , ,x y z tho mn 0 , , 1x y z v 2x y z . Tm gi tr nh nht ca

biu thc: A = 2 2 2( 1) ( 1) ( 1)x y z

z x y

CHNH THC


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S gio dc v o to ph th

K thi tuyn sinh vo lp 10 Trung hc ph thng

Nm hc 2011-2012

MN TOA N Thi gian 120 khng k thi gian giao

Ngy thi : 01 thng 7 nm 2011( t 1)

-----------------------------------

Cu 1 (2,5 im)

a) Rt gn 4:36392 A b) Gii bt phng trnh : 3x-2011



S GIO DC V O TO K THI TUYN SINH LP 10 THPT QUNG NAM NM HC 2011-2012 Kha thi : Ngy 30 thng 6 nm 2011

Mn thi TON ( chung cho tt c cc th sinh) Thi gian 120 pht (khng k thi gian giao ) Bi 1 (2.0 im )

Rt gon cc biu thc sau : A = 2 5 3 45 500 B = 1 15 12

3 2 5 2

Bi 2 (2.5 im )

1) Gii h phng trnh : 3 1

3 8 19

x y

x y

2) Cho phng trnh bc hai : x2 mx + m 1 = 0 (1) a) Gii phng trnh (1) khi m = 4 . b) Tm cc gi tr ca m phng trnh (1) c hai nghim x1 ; x2 tha mn h thc :

1 2

1 2

1 1

2011

x x

x x

Bi 3 (1.5 im ) Cho hm s y = 1

4x

2

1) V th ( P) ca hm s . 2) Xc nh a v b ng thng ( d) : y = ax + b ct trc tung ti im c tung bng - 2 v ct th (P) ni trn ti im c honh bng 2. Bi 4 (4.0 im ) Cho na ng trn tm (O ;R) ,ng k nh AB.Gi C l im ch nh gia ca cung AB.Trn tia i ca tia CB ly im D sao cho CD = CB. OD ct AC ti M. T A , k AH vung gc vi OD ( H thuc OD). AH ct DB ti N v ct na ng trn (O,R) ti E .

1) Chng minh MCNH l t gic ni tip v OD song song vi EB. 2) Gi K l giao im ca EC v OD. Chng minh CKD CEB ,Suy ra C l trung im ca KE. 3) Chng minh tam gic EHK vung cn v MN // AB. 4) T nh theo R din t ch hnh trn ngoi tip t gic MCNH

======Ht======

CHNH THC


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S GIO DC V O TO

THI BNH

K THI TUYN SINH LP 10 THPT NM HC 2011 - 2012

Mn thi: TON

Thi gian lm bi: 120 pht ,khng k thi gian giao

Bi 1. (2,0 im)

Cho biu thc: 3 1 3

11 1

xA

xx x

vi 0, 1x x .

1. Rt gn A. 2) T nh gi tr ca A khi x = 223 .

Bi 2. (2,0 im)Cho h phng trnh : ( m l tham s ).

1. Tm m h phng trnh c nghim (x ;y) trong x = 2.

2. Tm m h phng trnh c nghim duy nht (x ;y) tho mn 2x + y = 9.

Bi 3. (2,0 im)Trong mt phng ta Oxy, cho parabol (P): y = x2 v ng thng (d): y=ax + 3 ( a l tham s ) www.VNMATH.com

1. V parabol (P). 2. Chng minh rng (d) lun ct (P) ti hai im phn bit.

3. Gi 1 2;x x l honh giao im ca (P) v (d), tm a x1 +2x2 = 3

Bi 4. (3,5 im)Cho ng trn O, ng k nh AB = 2R. im C nm trn tia i ca tia BA

sao cho BC = R. im D thuc ng trn tm O sao cho BD = R. ng thng vung gc

vi BC ti C ct AD ti M.

1. Chng minh rng:

a) T gic BCMD l t gic ni tip. b) AB.AC = AD. AM.

c) CD l tip tuyn ca ng trn tm O.

2. ng trn tm O chia tam gic ABM thnh hai phn, t nh din t ch phn tam gic

ABM nm ngoi ng trn tm O theo R.

Bi 5. (0,5 im)Cho a, b, c l cc s khng m tho mn a + b + c = 1006.

Chng minh rng: 220122

)(2012

2

)(2012

2

)(2012

222

ba

cac

bcb

a .

CHNH THC

6

mx 2y 18

x - y


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S GIO DC V O TO QUNG NINH

K THI TUYN SINH LP 10 THPT NM HC 2011-2012

THI CHNH THC MN : TON

Ngy thi : 29/6/2011

Bi 1. (2,0 im) 1. Rt gn cc biu thc sau:

a) A = 2

1 2 1 b)B = 1 1

5 32 3 2 3

2.Bit rng th ca hm s y = ax - 4 i qua im M(2;5). Tm a Bi 2. (2,0 im)

1. Gii cc phng trnh sau:

a) 2 3 2 0x x b) 4 22 0x x

2.Cho phng trnh: 2 2( 1) 2 2 0x m x m vi x l n s.

a)Chng minh rng phng trnh lun c hai nghim phn bit vi mi m . b) Gi hai nghim ca phng trnh l x1 , x2 , t nh theo m gi tr ca biu thc

E = 21 22 1 2 2x m x m Bi 3 . (2im) Gii bi ton sau bng cch lp h phng trnh: Nh Mai c mt mnh vn trng rau bp ci . Vn c nh thnh nhiu lung mi lung cng trng mt s cy bp ci . Mai t nh rng : nu tng thm 7 lung rau nhng mi lung trng t i 2 cy th s cy ton vn t i 9 cy , nu gim i 5 lung nhng mi lung trng tng thm 2 cy th s rau ton vn s tng thm 15 cy . Hi vn nh Mai trng bao nhiu cy bp ci ? Bi 4 . (3,0 im) Cho ng trn (O) ng k nh AB v mt im C c nh trn bn k nh OA (C khc A v O) , im M di ng trn ng trn (M khc A,B) . Qua M k ng thng vung gc vi CM , ng thng ny ct cc tip tuyn ti A v B ca ng trn (O) ln lt ti D v E .

a) Chng minh ACMD v BCME l cc t gic ni tip . b) Chng minh DCEC. c) Tm v tr ca im M din t ch t gic ADEB nh nht .

Cu 5. (1,0 im) Tm cc b s thc (x, y, z) tho mn :

1

29 2 6 3 2011 10162

x y z x y z


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UBND TNH AN GIANG THI TUYN SINH VO LP 10 THPT S GIO DC-O TO NM HC 2011-2012 -------------- -------------------

Bi 1 (2,0 im) (khng c dng my t nh)

1-Thc hin php t nh : 12 75 48 : 3

2-Trc cn thc mu :1 5

15 5 3 1

Bi 2 (2,5 im) 1-Gii phng trnh : 2x2 5x 3 = 0

2-Cho h phng trnh ( m l tham s ) :

mx y = 3

x + 2my = 1

a. Gii h phng trnh khi m = 1. b.Tm gi tr ca m h phng trnh c nghim duy nht. Bi 3 (2,0 im )

Trn cng mt mt phng ta , cho parabol (P): y=2

x

2v ng thng (d):

3

2y x

1.Bng php t nh, hy tm ta giao im ca (P) v (d) . 2.Tm m ng thng (d) :y= mx m tip xc vi parabol (P) Bi 4 (3,5 im) Cho ng trn (O;r) v hai ng k nh AB,CD vung gc vi nhau.Trn cung nh DB, ly im N ( N khc B v D).Gi M l giao im ca CN v AB. 1-Chng minh ODNM l t gic ni tip. 2-Chng minh AN.MB =AC.MN. 3-Cho DN= r .Gi E l giao im ca AN v CD.T nh theo r di cc on ED, EC . HT


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S GD-T QUNG BNH TUYN SINH VO 10 THPT NM HC 2011-

2012

Kha ngy 01-7-2011

Mn: Ton

Thi gian 120 pht

Cu 1 ( 2 im) Cho Phng trnh x2 - 2(n-1)x 3 = 0 ( n tham s) a) Gii phng trnh khi n = 2.

b) Gi x1: x2 l hai nghim ca phng trnh. Tm n 1 2 4x x

Cu 2 ( 2 im) Cho biu thc 1

1

xQ

x x x

vi x>0 v 1x

a) Thu gn Q b) Tm cc gi tr ca x R sao cho 1

9x v Q c gi tr nguyn.

Cu 3 (1,5im) Cho ba ng thng (l1), ( l2), (l3) 1 2 3( ) : 2 1, ( ) : , ( ) : 3l y x l y x l y mx

a) Tim ta giao im B ca hai ng thng (l1) v ( l2). b) Tm m ba ng thng (l1), ( l2), (l3) ng quy.

Cu 4 (1 im) cho x,y cc s dng v 1 1

1x y

Chng minh bt ng thc: 1 1x y x y

Cu 5 ( 3,5 im) Cho ng trn (O), ng k nh MN v dy cung PQ vung gc vi MN Ti I ( khc M, N). trn cung nh NP ly im J (khc N, P). Ni M vi J ct PQ ti H.

a) Chng minh: MJ l phn gic ca gc PJQ .

b) Chng minh: t gic HINJ ni tip. c) Gi giao im ca PN vi MJ l G; JQ vi MN l K. Chng minh GK// PQ. d) Chng minh G l tm ng trn ni tip PKJ .

CHNH THC


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UBND TNH THI NGUYN THI TUYN SINH LP 10 THPT

S GIO DC V O TO NM HC 2011-2012 Mn thi: Ton HC Thi gian lm bi: 120 pht (khng k thi gian giao )

Bi 1:Rt gn biu thc A = 2 22

5 (1 4 4 )2 1

a a aa

, vi a > o,5.

Bi 2: Khng dng my tnh cm tay,hy gii phng trnh : 29x

2 -6x -11 = o

Bi 3 : Khng dng my tnh cm tay,hy gii h phng trnh:

2011 3 12011 2011 0x yx y Bi 4: Cho hm s bc nht y =f(x) = 2011x +2012. Cho x hai gi tr bt k x1, x2 sao cho x1 < x2.

a. Hy chng minh f(x1) < f(x2) b. Hm s ng bin hay nghch bin trn R ?

Bi 5 :Qua th ca hm s y = - 0,75x2,hy cho bit khi x tng t -2 n 4 th gi tr nh nht v gi tr ln nht ca y l bao nhiu ? Bi 6: Hy sp xp cc t s lng gic sau theo th t tng dn ,gii thch ? Cos47

0, sin 78

0, Cos14

0, sin 47

0, Cos87

0

Bi 7:Cho htam gic c gc bng 450.ng cao chia mt cnh k vi gc thnh cc phn 20cm v 21cm . Tnh cnh ln trong hai cnh cn li . Bi 8: Cho ng trn O bn knh OA v ng trn ng knh OA. a.Xc nh v tr tng i ca hai ng trn . b.Dy AD ca ng trn ln ct ng trn nh ti C.Chng minh nrng AC = CD . Bi 9: Cho A,B,C, l ba im trn mt ng trn.Atl tip tuyn ca ng trn ti A .ng thng song song vi At ct AB ti M v ct AC ti N. Chng minh rng : AB.AM =AC.AN Bi 10: Dng v nu cch dng tam gic ABC bit BC = 6cm,gc A bng 600 v ng cao AH = 3cm

chnh thc


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s gio dc v o to K THI TUYN SINH lp 10 THPT

Lng sn NM hc 2011 - 2012

MN THI: TON

chnh thc Thi gian lm bi: 120 pht khng k thi gian giao

Cu 1 (2 im):

a. T nh gi trij ca cc biu thc: A = 25 9 ; B = 2( 5 1) 5

b. Rt gn biu thc: P = 2 1

:x y xy

x y x y

Vi x>0, y>0 v x y.

T nh gi tr ca biu thc P ti x = 2012 v y = 2011.

Cu 2 ((2im): V trn cng mt h trc ta , th ca cc hm s y = x2 v y = 3x 2. T nh ta cc giao im ca hai th trn. Cu 3 (2 im):

a. T nh di cc cnh ca hnh ch nht, bit chiu di hn chiu rng 1 m v di mi ng cho ca hnh ch nht l 5 m.

b. Tm m phng trinh x - 2 x + m = 0 c hai nghim phn bit. Cu 4 (2 im) Cho ng trn (O; R) v im A nm ngoi ng trn. V cc tip tuyn AB, AC vi ng trn (B,C l nhng tip im).

a. Chng minh ABOC l t gic ni tip. Nu cch v cc tip tuyn AB, AC. b. BD l ng k nh ca ng trn (O; R). Chng minh: CD//AO. c. Cho AO = 2R, t nh bn k nh ng trn ni tip tam gic ABC.

Cu 5 (2 im) Tm s t nhin n bit: n + S(n) = 2011, trong S(n) l tng cc ch s ca n.


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S GIO DC V O TO TY NINH *********

K THI TUYN SINH LP 10 NM HC 2011 2012 ***************

Ngy thi: 02 thng 7 nm 2011 Mn thi: Ton (khng chuyn)

Thi gian: 120 pht (khng k thi gian giao ) -----------------------------------------------------------------------------------------------------

THI CHNH THC Cu 1: (1,5im)

Cho biu thc x 1 1 2

A : (x 0;x 1)x 1x 1 x x x 1

a) Rt gn biu thc A. b) Tm cc gi tr ca x sao cho A



S gio dc v o to

bc giang

chnh thc

thi tuyn sinh lp 10thpt

Nm hc 2011 - 2012

Mn thi: ton

Ngy thi: 01/ 7/ 2011

Thi gian lm bi: 120 pht

(Khng k thi gian giao )

Cu 1: (2,0 im)

1. Tnh 3. 27 144 : 36 .

2. Tm cc gi tr ca tham s m hm s bc nht y = (m - 2)x + 3 ng bin trn R.

Cu 2: (3,0 im)

1. Rt gn biu thc 3 1

2 13 1

a a aA

a a

, vi a0; a 1.

2. Gii h ph-ng trnh: 2 3 13

2 4

x y

x y

.

3. Cho ph-ng trnh: 2 4 1 0x x m (1), vi m l tham s. Tm cc gi tr ca m

ph-ngg trnh (1) c hai nghim 1 2,x x tho mn 2

1 2 4x x .

Cu 3: (1,5 im)

Mt mnh v-n hnh ch nht c din tch 192 m2. Bit hai ln chiu rng ln hn chiu di 8m. Tnh kch th-c ca hnh ch nht . Cu 4: (3 im)

Cho na -ng trn (O), -ng knh BC. Gi D l im c nh thuc on thng OC (D khc O v C). Dng -ng thng d vung gc vi BC ti im D, ct na -ng trn (O) ti im A. Trn cung AC ly im M bt k (M khc A v C), tia BM ct -ng thng d ti im K, tia CM ct -ng thng d ti im E. -ng thng BE ct na -ng trn (O) ti im N (N khc B). 1. Chng minh t gic CDNE ni tip. 2.Chng minh ba im C, K v N thng hng. 3. Gi I l tm -ng trn ngoi tip tam gic BKE. Chng minh rng im I lun nm trn mt -ng thng c nh khi im M thay i.

Cu 5: (0,5 im)

Cho hai s thc d-ng x, y tho mn:

3 3 2 2 2 2 3 33 4 4 0x y xy x y x y x y x y . Tm gi tr nh nht ca biu thc M = x + y.

----------------------------------------Ht------------------------------------------

Cn b coi thi khng gii thch g thm !

H v tn th sinh: ..................S bo danh:............... Gim th 1 (H v tn):...............................................

Gim th 2 (H v tn):...............................................


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S GIO DC V O TO BNH THUN

---------------------------

K THI TUYN SINH LP 10 THPT NM HC 2011 2012

Mn thi : TON

Thi gian lm bi : 120 pht ( khng k thi gian pht )

Bi 1:( 2 im) Cho hm s y = -x 2 c th l ng thng (d )

1/ Trong mt phng ta Oxy hy v ng thng ( d ) 2/ Hm s y = 2mx + n c th l ng thng ( d ). Tm m v n hai ng thng

(d) v ( d ) song song vi nhau.

Bi 2 : (2 im) Gii phng trnh v h phng trnh sau:

1/ 3x2 + 4x + 1 = 0

2/

x - 2y 4

2x 3y 1

Bi 3 : (2 im) Rt gn cc biu thc sau:

1/ A = ( 32 3 18) : 2

2/ B = 15 12 6 2 6

5 2 3 2

Bi 4 : (4 im) Cho ng trn (O; R) v im A sao cho OA = 2R. T A v hai tip tuyn AB, AC

n (O) ( vi B,C l cc tip im). 1/ Tnh gc AOB.

2/ T A v cc tuyn APQ n ng trn (O) ( Ct tuyn APQ khng i qua tm O . Gi H l trung im ca PQ ; BC ct PQ ti K .

a/ Chng minh 4 im O, H , B, A cng thuc mt ng trn. b/ Chng minh AP. AQ = 3R2.

c/ Cho OH = 2

R, t nh di on thng HK theo R

--------------------- Ht-------------------

CHNH THC


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S GIO DC O TO NINH THUN

K THI TUYN SINH VO LP 10 THPT NM HC 2011 2012 Kha ngy: 26 6 2011

Mn thi: TON


:

Bi 1: (2,0 im) Cho ng thng (d): y = -x + 2 v parabol (P): y = x2

a) V (d) v (P) trn cng mt h trc ta . b) Bng th hy xc nh ta cc giao im ca (d) v (P).

Bi 2: (2,0 im) a) Gii phng trnh: 3x2 4x 2 = 0.

b) Gii h phng trnh:

42

123

yx

yx

Bi 3: (2,0 im)

Cho biu thc: P = )1(342

8x

xx

xx

, vi x 0

a) Rt gn biu thc P.

b) Tm cc gi tr nguyn dng ca x biu thc Q = P

P

1

2 nhn gi tr

nguyn.

Bi 4: (3,0 im) Cho tam gic ABC c gc BAC = 60

0, ng phn gic trong ca gc ABC l BD v ng phn gic trong ca gc ACB l CE ct nhau ti I (D AC v E AB)

a) Chng minh t gic AEID ni tip c trong mt ng trn. b) Chng minh rng: ID = IE. c) Chng minh rng: BA.BE = BD. BI

Bi 5: (1,0 im) Cho hnh vung ABCD. Qua im A v mt ng thng ct cnh BC ti E v ct ng thng CD ti F. Chng minh rng:

222

111

FA


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S GD&T THNH PH H NI

THI TUYN SINH VO LP 10

Mn thi : Ton

Ngy thi : 22 thng 6 nm 2011


Bi I (2,5 im)

Cho x 10 x 5

Ax 25x 5 x 5

Vi x 0,x 25 .

1) Rt gn biu thc A.

2) T nh gi tr ca A khi x = 9.

3) Tm x 1

A3

.

Bi II (2,5 im)

Gii bi ton sau bng cch lp phng trnh hoc h phng trnh:

Mt i xe theo k hoch ch ht 140 tn hng trong mt s ngy quy nh. Do mi ngy i ch vt mc 5 tn nn i hon thnh k hoch sm hn thi gian quy nh 1 ngy v ch thm c 10 tn. Hi theo k hoch i xe ch hng ht bao nhiu ngy?

Bi III (1,0 im)

Cho Parabol (P): 2y x v ng thng (d): 2y 2x m 9 .

1) Tm to cc giao im ca Parabol (P) v ng thng (d) khi m = 1.

2) Tm m ng thng (d) ct Parabol (P) ti hai im nm v hai ph a ca trc tung.

Bi IV (3,5 im)

Cho ng trn tm O, ng k nh AB = 2R. Gi d1 v d2 l hai tip tuyn ca ng trn (O) ti hai im A v B.Gi I l trung im ca OA v E l im thuc ng trn (O) (E khng trng vi A v B). ng thng d i qua im E v vung gc vi EI ct hai ng thng d1 v d2 ln lt ti M, N.

1) Chng minh AMEI l t gic ni tip.

2) Chng minh ENI EBI v 0MIN 90 .

3) Chng minh AM.BN = AI.BI .

4) Gi F l im ch nh gia ca cung AB khng cha E ca ng trn (O). Hy t nh din t ch ca tam gic MIN theo R khi ba im E, I, F thng hng.

Bi V (0,5 im)

Vi x > 0, tm gi tr nh nht ca biu thc: 2 1M 4x 3x 2011

4x .

CHNH THC


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S gio dc & o to H-ng Yn

- - - - - - - - - - - - - - - -

( thi c 02 trang)

K thi tuyn sinh vo lp 10 THPT

Nm hc 2011 2012 Mn thi: Ton

Thi gian: 120 pht (khng k giao )

Ngy thi: 05 thng 7 nm 2011

-------------------------------------------

Phn A. Trc nghim khch quan (2)

T cu 1 n cu 8, hy chn ph-ng n ng v vit ch ci ng tr-c ph-ng n

vo bi lm.

Cu 1: Gi tr ca biu thc 18a (vi a 0) bng:

A. 9 a B. 3a 2 C. 2 3a D. 3 2a

Cu 2: Biu thc 2 2 3x x c ngha khi v ch khi: A. 3x B. 1x C. 1x D. 1x

Cu 3: im M(- 1; 2) thuc th hm s y = 2

ax khi a bng: A. 2 B. 4 C. - 2 D. 0,5

Cu 4: Gi S, P l tng v tch cc nghim ca ph-ng trnh 2 8 7 0x x . Khi S + P

bng:

A. - 1 B. - 15 C. 1 D. 15

Cu 5: Ph-ng trnh x2 (a + 1)x + a = 0 c nghim l:

A. 1 21;x x a B. 1 21;x x a C. 1 21;x x a D.

1 21;x x a

Cu 6: Cho -ng trn (O; R) v -ng thng (d). Bit rng (d) v -ng trn (O; R) khng

giao nhau, khong cch t O n (d) bng 5. Khi :

A. R < 5 B. R = 5 C. R > 5 D. R 5 Cu 7: Tam gic ABC vung ti A, AC = 3cm, AB = 4cm. Khi sinB bng:

A. 3

4 B.

3

5 C.

4

5 D.

4

3

Cu 8: Mt hnh nn c chiu cao h v -ng knh y d . Th tch ca hnh nn l:

A. 21

3d h B. 2

1

4d h C. 2

1

6d h D. 2

1

12d h

Phn B: T lun (8)

Bi 1: (1,5):

a) Rt gn biu thc: P = (4 2 8 2). 2 8

b) Tm to giao im ca hai th hm s 2

y x v 3 2y x

Bi 2: (1): Mt cng ty vn ti iu mt s xe ti n kho hng ch 21 tn hng. Khi n

kho hng th c 1 xe b hng nn ch ht l-ng hng , mi xe phi ch thm 0,5 tn so vi d nh ban u. Hi lc u cng ty iu n kho hng bao nhiu xe. Bit rng khi l-ng hng ch mi xe l nh- nhau.

Bi 3: (1,5): Cho h ph-ng trnh:

( 1) 3 1

2 5

m x my m

x y m

chnh thc


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a) Gii h ph-ng trnh vi m = 2

b) Tm m h ph-ng trnh c nghim duy nht ( ; )x y sao cho 2 2 4x y

Bi 4: (3) Cho -ng trn tm O bn knh R v mt -ng thng (d) c nh, (d) v -ng

trn (O; R) khng giao nhau. Gi H l chn -ng vung gc k t O n -ng thng (d), M

l mt im thay i trn (d) (M khng trng vi H). T M k hai tip tuyn MA v MB vi

-ng trn (A, B l cc tip im). Dy cung AB ct OH ti I.

a) Chng minh 5 im O, A, B, H, M cng nm trn mt -ng trn.

b) Chng minh IH.IO = IA.IB

c) Chng minh khi M thay i trn (d) th tch IA.IB khng i.

Bi 5: (1): Tm gi tr ln nht ca biu thc

24( 1) 3 2 1y x x x vi 1 < x < 1.


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S GD&T VNH PHC

CHNH THC

K THI TUYN SINH VO LP 10 THPT NM HC 2011 2012

THI MN: TON (Thi gian lm bi: 120 pht, khng k thi gian giao )

PHN I: TRC NGHIM (2 im)Trong 4 cu: t cu 1 n cu 4, mi cu u c 4 la chn, trong ch c duy nht mt la chn ng. Em hy vit vo t giy lm bi thi ch ci A, B, C hoc D ng trc la chn m em cho l ng (V d: Nu cu 1 em la chn l A th vit l 1.A)

Cu 1. Gi tr ca 12. 27 bng:

A. 12 B. 18 C. 27 D. 324

Cu 2. th hm s y= mx + 1 (x l bin, m l tham s) i qua im N(1; 1) . Khi g tr ca m bng: A. m = - 2 B. m = - 1 C. m = 0 D. m = 1

Cu 3. Cho tam gic ABC c din t ch bng 100 cm2 . Gi M, N, P tng ng l trung im ca AB, BC, CA. Khi din t ch tam gic MNP bng: A. 25 cm

2 B. 20 cm

2 C. 30 cm

2 D. 35 cm

2

Cu 4. Tt c cc gi tr x biu thc x 1 c ngha l: A. x < 1 B. x 1 C. x > 1 D. x1

PHN II. T LUN (8 im)

Cu 5. (2.0 im) Gii h phng trnh 2

x y 0

x 2y 1 0

Cu 6. (1.5 im) Cho phng trnh x2 2mx + m2 1 =0 (x l n, m l tham s). a) Gii phng trnh vi m = - 1 b) Tm tt c cc gi tr ca m phng trnh (1) c hai nghim phn bit c) Tm tt c cc gi tr ca m phng trnh (1) c hai nghim x1 , x2 sao cho tng P =

x12 + x2

2 t

gi tr nh nht. Cu 7. (1.5 im) Mt hnh ch nht ban u c cho vi bng 2010 cm. Bit rng nu tng chiu di ca hnh ch nht thm 20 cm v tng chiu rng thm 10 cm th din t ch hnh ch nht ban u tng ln 13 300 cm2. T nh chiu di, chiu rng ca hnh ch nht ban u. Cu 8. (2.0 im) Cho tam gic ABC c ba gc nhn, khng l tam gic cn, AB < AC v ni tip ng trn tm O, ng k nh BE. Cc ng cao AD v BK ca tam gic ABC ct nhau ti im H. ng thng BK ct ng trn (O) ti im th hai l F. Gi I l trung im ca cnh AC. Chng minh rng:

a) T gic AFEC l hnh thang cn. b) BH = 2OI v im H i xng vi F qua ng thng AC.

Cu 9.(2.0 im) Cho a, b, c l ba s thc dng tha mn iu kin a + b + c = 1. Tm gi tr

ln nht ca biu thc: P = ab bc ca

c ab a bc b ca

.

-----HT-----

Cn b coi thi khng gii thch g thm! H v tn th sinh:


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S GIO DC V O TO K THI TUYN SINH LP 10 TRUNG HC PH

THNG

THNH PH NNG Kha ngy 21 thng 6 nm 2011

CHNH THC MN THI: TON Thi gian :120 pht (khng tnh thi gian giao )

Bi 1: (2,0im) a/ Gii phng trnh (2x + 1)(3 x) + 4 = 0

b/ Gii h phng trnh 3x - y = 1

5x + 3y = 11

Bi 2: (1 )

Rt gn biu thc Q = 35

2:

15

55

12

36

Bi 3: (2) Cho phng trnh x2 2x 2m2 = 0 ( m l tham s ) a/ Gii phng trnh khi m = 0 b/ Tm m phng trnh c hai nghim x1;x2 khc 0 v tha iu kin x1

2 =4x2

2

Bi 4: (1,5) Mt hnh ch nht c chu vi bng 28 cm v mi ng cho ca n c di 10cm . Tm di cc cnh ca hnh ch nht .

Bi 5: (3,5) Cho tam gic u ABC ni tip ng trn ng k nh AD . Gi M l mt im di ng trn cung nh AB ( M khng trng vi cc im A v B) a/ Chng minh rng MD l ng phn gic ca gc BMC b/ Cho AD = 2R . T nh din t ch t gic ABDC theo R c/ Gi K l giao im ca AB v MD , H l giao im ca AD v MC Chng minh rng ba ng thng AM,BD,HK ng quy.

HT


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S GIO DC V O TO K THI TUYN SINH LP 10 THPT

TP.HCM Nm hc: 2011 2012

CHNH THC MN: TON


Bi 1: (2 im) Gii cc phng trnh v h phng trnh sau:

a) 23 2 1 0x x

b) 5 7 3

5 4 8

x y

x y

c) 4 25 36 0x x

d) 23 5 3 3 0x x

Bi 2: (1,5 im)

a) V th (P) ca hm s 2y x v ng thng (D): 2 3y x trn cng mt h

trc to . b) Tm to cc giao im ca (P) v (D) cu trn bng php t nh.

Bi 3: (1,5 im) Thu gn cc biu thc sau:

3 3 4 3 4

2 3 1 5 2 3A

2 28 4 8

3 4 1 4

x x x x xB

x x x x

( 0, 16)x x

Bi 4: (1,5 im)

Cho phng trnh 2 22 4 5 0x mx m (x l n s) a) Chng minh rng phng trnh lun lun c nghim vi mi m. b) Gi x1, x2 l cc nghim ca phng trnh.

Tm m biu thc A = 2 21 2 1 2x x x x . t gi tr nh nht

Bi 5: (3,5 im) Cho ng trn (O) c tm O, ng k nh BC. Ly mt im A trn ng trn (O) sao cho AB > AC. T A, v AH vung gc vi BC (H thuc BC). T H, v HE vung gc vi AB v HF vung gc vi AC (E thuc AB, F thuc AC).

a) Chng minh rng AEHF l hnh ch nht v OA vung gc vi EF. b) ng thng EF ct ng trn (O) ti P v Q (E nm gia P v F). c) Chng minh AP2 = AE.AB. Suy ra APH

Gi I l giao im ca KF v BC. Chng minh IH2 = IC.ID l tam gic cn d) Gi D l giao im ca PQ v BC; K l giao im ca AD v ng trn (O) (K

khc A). Chng minh AEFK l mt t gic ni tip.


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S GIO DC V O TO K THI TUYN SINH VO LP 10

TRUNGHC PH THNG K LK NM HC: 2011 2012

THI CHNH THC Mn thi: Ton Thi gian lm bi: 120 pht, khng k thi gian giao

Cu 1. (2,0 im) 3) Gii cc phng trnh sau:

a/ 9x2 + 3x 2 = 0.

b/ x4 + 7x

2 18 = 0.

4) Vi gi tr no no ca m th th ca hai hm s y = 12x + (7 m) v y = 2x + (3 + m) ct nhau ti mt im trn trc tung?

Cu 2. (2,0 im)

1) Rt gn biu thc: 2 1

.1 2 3 2 2

A

2) Cho biu thc: 1 1 1 2

1 . ; 0, 111 1

B x xxx x x

a) Rt gn biu thc B. b) Tm gi ca ca x biu thc B = 3.

Cu 3.(1,5 im)

Cho h phng trnh: 2 1

(1)2 2

y x m

x y m

1) Gii h phng trnh (1) khi m =1. 2) Tm gi tr ca m h phng trnh (1) c nghim (x ; y) sao cho biu thc P = x

2 + y

2 t gi tr nh nht.

Cu 4.(3,5 im) Cho tam gic ABC c ba gc nhn ni tip ng trn (O). Hai ng cao BD v CE ca tam gic ABC ct nhau ti im H. ng thng BD ct ng trn (O) ti im P; ng thng CE ct ng trn (O) ti im th hai Q. Chng minh rng:

1) BEDC l t gic ni tip. 2) HQ.HC = HP.HB 3) ng thng DE song song vi ng thng PQ. 4) ng thng OA l ng trung trc ca on thng P.

Cu 5. (1,0 im) Cho x, y, z l ba s thc ty . Chng minh: x2 + y2 + z2 yz 4x 3y -7.

-------------------- Ht -------------------- Th sinh khng c s dng ti liu. Gim th khng c gii thch g thm.

H v tn th sinh:.. S bo danh:


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Ch k gim th I: ..Ch k gim th 2:


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S GIO DC V O TO NGH AN

K THI TUYN SINH VO LP 1 THPT NM HC 2011 2012

Mn thi: TON

Thi gian lm bi : 120 pht(khng k thi gian giao )

Cu 1: (3,0 im)

Cho biu thc A = 21

1:

1

11

x

x

xxx

a) Nu iu kin xc nh v rt biu thc A

b) Tim gi tr ca x A = 3

1.

c) Tm gi tr ln nht cua biu thc P = A - 9 x

d)

Cu 2: (2,0 im)

Cho phng trnh bc hai x2 2(m + 2)x + m2 + 7 = 0 (1) (m l tham s)

a) Gii phng trnh (1) khi m = 1.

b) Tm m phng trnh (1) c nghim x1, x2 tha mn x1x2 2(x1 + x2) = 4

c)

Cu 3: (1,5 im)

Qung ng AB di 120 km. Hi xe my khi hnh cng mt lc i t A n B. Vn tc ca

xe my th nht ln hn vn tc ca xe my th hai l 10 km/h nn xe my th nht n B

trc xe my th hai 1 gi. T nh vn tc ca mi xe ?

Cu 4: (3,5 im)

Cho im A nm ngoi ng trn (O). T A k hai tip tuyn AB, AC v ct tuyn ADE ti

ng trn (B, C l hai tip im; D nm gia A v E). Gi H l giao im ca AO v BC.

a) Chng minh rng ABOC l t gic ni tip

b) Chng minh rng AH.AO = AD.AE

c) Tip tuyn ti D ca ng trn (O) ct AB, AC theo th t ti I v K. Qua im O k

ng thng vung gc vi OA ct tia AB ti P v ct tia AC ti Q.

Chng minh rng IP + KQ PQ.

----- Ht ------

H v tn th sinh :S bo danh..

CHNH THC


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KHNH HA NM HC 2011 - 2012 Ngy thi : 21/06/2011 Mn thi: TON


Bi 1( 2 im)

1) n gin biu thc: A 2 3 6 8 4

2 3 4

2) Cho biu thc:

1 1( );( 1)

1 1P a a

a a a a

Rt gn P v chng t P 0

Bi 2( 2 im) 1) Cho phng trnh bc hai x2 + 5x + 3 = 0 c hai nghim x1; x2. Hy lp mt phng

trnh bc hai c hai nghim (x12 + 1 ) v ( x2

2 + 1).

2) Gii h phng trnh

2 34

2

4 11

2

x y

x y

Bi 3( 2 im) Qung ng t A n B di 50km.Mt ngi d nh i xe p t A n B vi vn tc khng i.Khi i c 2 gi,ngi y dng li 30 pht ngh.Mun n B ng thi gian nh,ngi phi tng vn tc thm 2 km/h trn qung ng cn li.T nh vn tc ban u ca ngi i xe p.

Bi 4( 4 im) Cho tam gic ABC c ba gc nhn v H l trc tm.V hnh bnh hnh BHCD.ng thng i qua D v song song BC ct ng thng AH ti E.

1) Chng minh A,B,C,D,E cng thuc mt ng trn 2) Chng minh BAE DAC 3) Gi O l tm ng trn ngoi tip tam gic ABC v M l trung im ca BC,ng

thng AM ct OH ti G.Chng minh G l trng tm ca tam gicABC. 4) Gi s OD = a.Hy t nh di ng trn ngoi tip tam gic BHC theo a

THI CHNH THC ( thi c 01 trang)


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S GIO DC V O TO THI TUYN SINH VO LP 10 THPT

QUNG TR Kha ngy 27 thng 6 nm 2011

MN: TON

Thi gian: 120 pht (khng k thi gian giao )

Cu 1 (2,0 im) Rt gn cc biu thc (khng s dng my t nh cm tay):

a) 27 5 12 2 3M ;

b) 1 1

:42 2

aN

aa a

, vi a > 0 v 4a .

Cu 2 (1,5 im) Gii cc phng trnh (khng s dng my t nh cm tay):

a) 2 5 4 0x x ;

b) 1 1

23

x

x

.

Cu 3 (1,0 im) a) V th (d) ca hm s y = -x + 3; b) Tm trn (d) im c honh v tung bng nhau.

Cu 4 (1,0 im) Gi x1, x2 l hai nghim ca phng trnh x

2 + 3x -5 = 0. T nh gi tr ca biu thc

2 2

1 2x x .

Cu 5 (1,5 im) Gii bi ton bng cch lp h phng trnh: T nh chu vi ca mt hnh ch nht, bit rng nu tng mi chiu ca hnh ch nht thm 4m th din t ch ca hnh ch nht tng thm 80m2 ; nu gim chiu rng 2m v tng chiu di 5m th din t ch hnh ch nht bng din t ch ban u. Cu 6 (3,0 im) Cho t gic ABCD ni tip na ng trn (O) ng k nh AD. Hai ng cho AC v BD ct nhau ti E. K FE vung gc vi AD (FAD; F O).

a) Chng minh: T gic ABEF ni tip c; b) Chng minh: Tia CA l tia phn gic ca gc BCF; c) Gi M l trung im ca DE. Chng minh: CM.DB = DF.DO.

--------------------HT-------------------

H v tn th sinh: ..S bo danh:..

CHNH THC


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S GIO DC O TO K THI TUYN SINH VO LP 10 TRUNG HC PH THNG

BNH NH KHA NGY :29/06/2011 chnh thc Mn thi: Ton Thi gian : 120 pht ( Khng k thi gian pht ) Ngy thi: 30/6/2011

Bi 1 (2im)

c) Gii h phng trnh : 3 7

2 8

x y

x y

d) Cho hm s y = ax + b.Tm a v b bit rng th ca hm s cho song song vi ng thng y = -2x +3 v i qua im M( 2;5)

Bi 2: (2im)

Cho phng trnh 2 2( 1) 4 0x m x m (m l tham s)

a)Gii phng trnh khi m = -5 b)Chng minh rng phng trnh lun c hai nghim phn bit vi mi m c)Tm m sao cho phng trnh cho c hai nghim x1, x2 tha mn h thc

2 2

1 2 1 23 0x x x x

Bi 3 : (2im) Mt mnh t hnh ch nht c chiu di hn chiu rng 6m v bnh phng di ng cho gp 5 ln chu vi.T nh din t ch hnh ch nht Bi 4: (3im) Cho ng trn tm O, v dy cung BC khng i qua tm.Trn tia i ca tia BC ly im M bt k.ng thng i qua M ct ng (O) ln lt ti hai im N v P (N nm gia M v P) sao cho O nm bn trong gc PMC. Trn cung nh NP ly im A sao cho cung AN bng cung AP.Hai dy cung AB,AC ct NP ln lt ti D v E. a)Chng minh t gic BDEC ni tip. b) Chng minh : MB.MC = MN.MP

c) Bn k nh OA ct NP ti K. Chng minh: 2 .MK MB MC Bi 5 (1im)

Tm gi tr nh nht ca biu thc: 2

2

2 2011x xA

x

(vi x 0


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S GD&T HA BNH

chnh thc

K THI TUYN SINH VO LP 10 THPT NM HC 2010-2011

THI MN TON LP CHT LNG CAO TRNG PT DTNT TNH

Ngy thi : 21 thng 7 nm 2010 Thi gian lm bi 150 pht (khng k thi gian giao )

( thi gm c 01 trang )

Cu 1 (2 im) Cho biu thc : 2

2 2 x - 6A = 1- + :

x - 2x - 2 x + 2

a) Tm x biu thc A c ngha ;

b) Rt gn biu thc A.

Cu 2 (2 im) Cho phng trnh : 2x - mx - x - m - 3 = 0 (1), (m l tham s).

a) Chng minh rng phng trnh (1) lun c hai nghim phn bit 1 2x ; x vi mi

gi tr ca m ;

b) Tm gi tr ca m biu thc 2 21 2 1 2 1 2P = x + x - x x + 3x + 3x t gi tr nh nht.

Cu 3 (2 im) Mt can i xui dng sng t bn A n bn B ht 6 gi, i ngc dng sng

t bn B v bn A ht 8 gi. (Vn tc dng nc khng thay i)

a) Hi vn tc ca can khi nc yn lng gp my ln vn tc dng nc chy ?

b) Nu th tri mt b na t bn A n bn B th ht bao nhiu thi gian ?

Cu 4 (3 im)

1. Cho tam gic ABC vung ti A v AB = 10cm. Gi H l chn ng cao k t A

xung BC. Bit rng HB = 6cm, t nh di cnh huyn BC.

2. Cho tam gic ABC ni tip ng trn (O), H l trc tm ca tam gic, AH ct ng

trn (O) ti D (D khc A). Chng minh rng tam gic HBD cn.

3. Hy nu cch v hnh vung ABCD khi bit tm I ca hnh vung v cc im M, N

ln lt thuc cc ng thng AB, CD. (Ba im M, I, N khng thng hng).

Cu 5 (1 im) Gii h phng trnh : 2 2

2 2 2 2

x y - xy - 2 = 0

x + y = x y

H v tn th sinh :................................ S bo danh : ............. ........... Phng thi : ........

Ht


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S GD t h tnh thi TS vo lp 10 Nm hc 2011 - 2012

Mn: Ton Thi gian: 120 pht

Cu 1: 2

a) Tm m -ng thng y = (2m 1)x + 3 song song vi -ng thng y = 3x -1.

b) Gii h pt:

132

42

yx

yx

Cu 2: 1,5 Cho biu thc: P =

1

2

2

1

2

1

aaa vi a> 0 , # 1.

a) Rt gn P b) Tm a P > 1 /2

Cu 3: (2 )

a) Tm ta giao im ca y = x2 v y = -x + 2.

b) Xc nh m pt: 2x - x+1- m=0 c hai nghim x1,2 tha mn

4( 03)11

21

21

xxxx

.

Cu 4: (3,5 ) Trn na -ng trn -ng knh BC, ly hai im M, N sao cho M thuc cung

BN. Gi A l giao im ca BM v CN. H l giao im ca BN v CM. a) CMR: t gic AMHN ni tip. b) CM : ABN ng dng HCN. c) Tnh gi tr ca S = BM.BA + CN.CA

Cu 5: ( 1 ) Cho a, b, c > 9/4 . Tm GTNN ca

Q = 323232

a

c

c

b

b

a

------------------------ht--------------------------


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S GIO DC & O TO K THI TUYN SINH LP 10 THPT THNH PH CN TH NM HC 2011-2012

Kha ngy 27/06/2011

CHNH THC MN TON (Thi gian lm bi : 120 pht)

Cu 1 (2 im) :

x+1- 2 x x+ x

x -1 x +1

1) Tm x biu thc A c ngha. 2) Rt gn biu thc A. 3) Vi gi tr no ca x th A < 1 ?

Cu 2 (2 im) :

Gii cc bt phng trnh v phng trnh sau : 1) 4 5x 16 2) x

2 + x 20 = 0 1 1 1

x+3 x+4 x+5

4) x 4x - 3 = 2

Cu 3 (1,5 im) :

Cho phng trnh 2x2 2mx + m 1 = 0 (1) 1) Chng minh phng trnh (1) c hai nghim phn bit vi mi gi tr ca m. 2) Xc nh m phng trnh (1) c hai nghim dng.

Cu 4 (1,5 im) :

Cho parabol (P) : y = ax2

1) Tm a bit rng parabol (P) i qua im A( 3 ; 3). V (P) vi a va tm c.

2) Xc nh gi tr ca m ng thng y = (2 m)x + 3m m2 to vi trc honh

mt gc = 60o.

Cu 5 (3 im) :

Cho tam gic ABC vung ti A c ng cao AH. V ng trn tm O ng

knh AH, n ct AB v AC ti E v F. Cc tip tuyn vi ng trn (O) ti E v F ln

lt ct cnh BC ti M v N. 1) Chng minh : T gic MEOH ni tip c. 2) Chng minh : AB.HE = AH.HB. 3) Chng minh : 3 im E, O, v F thng hng.

4) Cho AB = 2 10 cm; AC = 2 15 cm. Tnh din tch tam gic OMN.

(Ht)

K thi tuyn sinh ng Nai 2011 2012

Cho biu thc A = +

3) + =


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Cu I: 2, 5 1/ Gii PT 2x2 3x 2 = 0

2/ Gii HPT

032

73

yx

yx

3/ n gin biu thc 125805 P

4/ Cho bit )1;1(11 bababa . Chng minh a + b = ab

Lu : cc cu 1/, 2/ 3/ khng s dng my t nh. Cu II: 3,0

Cho Parapol y = x2 (P), v ng thng : y = 2(1 m)x + 3 (d), vi m l tham s.

1/ V th (P). 2/ Chng minh vi mi gi tr ca m, parapol (P) v ng thng (d) lun ct nhau ti hai

im phn bit 3/ Tm cc gi tr ca m, (P) v (d) ct nhau ti im c tung y = 1

Cu III: 3, 5 Cho (O), dng k nh AB = 2R, C l mt im trn ng trn ( khc A, B). Gi M l

trung im ca cung nh BC 1/ Chng minh AM l tia phn gic ca gc BAC 2/ Cho bit AC = R. T nh BC, MB 3/ Gi s BC ct AM N. Chng minh MN. MA = MC2

Cu IV: 1,0 Chng minh P= x4 2x3 + 2x2 2x + 1 0 , vi mi gi tr ca x.


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KHNH HA NM HC 2011 - 2012 Kha ngy : 29/06/2011

Mn : TON


i 1: (3.00im) ( Khng dung my t nh cm tay)

1. T nh gi tr biu thc: 1

A 32 3

2. Gii h phng trnh:

2x y 5

3x y 10

3. Gii phng trnh: x4 5x2 36 = 0

i 2: : (2.00 im )

Cho parapol (P) : y = 21

2x .

1. V (P) trong mt phng ta Oxy. 2. Bng phng php i s,hy tm ta cc giao im A v B ca (P) v ng thng

(d) : y = - x + 4.T nh din t ch tam gic AOB ( O l gc ta ).

i 3 : (1.00 im ) Cho phng trnh bc hai x2 - ( m + 1 )x + 3 ( m 2 ) = 0 ( m l tham s).Tm tt c cc gi tr ca m phng trnh c hai nghim x1;x2 tha mn iu kin x1

3 + x2

3 35.

i 4 : (4.00 im ) Cho na ng trn tm O ng k nh AB = 2R( k hiu l (O) ).Qua trung im I ca AO, v tia Ix vung gc vi AB v ct (O) ti K.Gi M l im di ng trn on IK(M khc I v K ), ko di AM ct (O) ti C.Tia Ix ct ng thng BC ti D v ct tip tuyn ti C ca (O) ti E.

1. Chng minh t gic IBCM ni tip. 2. Chng minh tam gic CEM cn ti E. 3. Khi M l trung im ca IK,t nh din t ch tam gic ABD theo R. 4. Chng t rng tm ng trn ngoi tip tam gic AMD thuc mt ng thng c nh

khi M thay i.

---------- HT ----------

THI CHNH THC


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thi chnh thc

B

S gd v o to k thi tuyn sinh vao lp 10 THPT

Thanh ho Nm hc : 2011 - 2012

Mn thi : Ton

Thi gian lm bi : 120 pht Ngy thi : 30 thng 6 nm 2011

Bi 1 : ( 1,5 im )

1. Cho hai s : b1 = 1 + 2 ; b2 = 1 - 2 . Tnh b1 + b2

2. Gii h ph-ng trnh

32

12

nm

nm

Bi 2 ( 1,5 im )

Cho biu thc B = 2

1:)

4

14

22(

bb

b

b

b

b

b vi b 0 v b 4

1. Rt gn biu thc B

2. Tnh gi tr ca B ti b = 6 + 4 2 Bi 3 ( 2,5 im )

Cho ph-ng trnh : x2 ( 2n -1 )x + n (n- 1) = 0 ( 1 ) vi n l tham s 1. Gii ph-ng trnh (1) vi n = 2 2. CMR ph-ng trnh (1) lun c hai nghim phn bit vi mi n 3. Gi x1 , x2 l hai nghim ca ph-ng trnh (1) ( v x1 < x2

Chng minh : x12 2x2 + 3 0 .

Bi 4 : ( 3 im )

Cho tam gic BCD c 3 gc nhn . Cc -ng cao CE v DF ct nhau ti H .

1. CM : T gic BFHE ni tip -c trong mt -ng trn

2. Chng minh BFE v BDC ng dng 3. K tip tuyn Ey ca -ng trn tm O -ng knh CD ct BH ti N . CMR N l trung

imca BH . Cu 5 : ( 1 im )

Cho cc s d-ng x, y , z . Chng minh bt ng thc :

2

yx

z

zx

y

zy

x


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S GD & O TO K THI TUYN SINH VO LP 10 THPT THANH HO Nm hc 2011-2012

Mn thi: Ton Thi gian lm bi: 120 pht Ngy thi 30 thng 6 nm 2011

Bi 1(1.5):

1. Cho hai s a1 = 1+ 2 ; a2 = 1- 2 . Tnh a1+a2.

2. Gii h phng trnh:

32

12

yx

yx

Bi 2(2): Cho biu thc A = 2

1:

4

14

22

aa

a

a

a

a

a (Vi a 0;a 4 )

1. Rt gn biu thc A.

2. T nh gi tr ca A ti a = 6+4 2 Bi 3(2,5): Cho phng trnh: x2 (2m-1)x + m(m-1) = 0 (1). (Vi m l tham s)

a. Gii phng trnh (1) vi m = 2. b. Chng minh rng phng trnh (1) lun c hai nghim phn bit vi mi m. c. Gi x1 v x2 l hai nghim ca phng trnh (1). (Vi x1 < x2). Chng minh rng x1

2 2x2 + 3 0.

Bi 4(3): Cho tam gic ABC c ba gc nhn. ng cao BD v CK ct nhau ti H. 1. Chng minh t gic AKHD ni tip c trong mt ng trn 2. Chng minh tam gic AKD v tam gic ACD ng dng. 3. k tip tuyn Dx ti D ca ng trn tm O ng k nh BC ct AH ti M. Chng minh

M l trung im ca AH Bi 5(1): Cho ba s dng a, b, c. Chng minh bt ng thc:

2

ba

c

ca

b

cb

a

========================Ht========================

thi chinh thc

a


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S GIO DC V O TO K THI TUYN SINH LP 10 NM HC 2011-2012

QUNG NGI MN : TON

Thi gian lm bi : 120 pht (khng k thi gian giao )

Bi 1: (1.5 im) 1) Thc hin php t nh: 2 9 + 3 16

2) Gii phng trnh v h phng trnh sau: a) x

2 20x + 96 = 0 x + y = 4023

b) x y = 1

Bi 2: (2.5im) 1) Cho hm s y = x2 c th l (P) v ng thng (d): y = x + 2

a) V ( P ) v ( d ) trn cng mt h to Oxy

b) Bng php t nh hy tm to giao im ca ( P ) v ( d )

2) Trong cng mt h to Oxy cho 3 im: A(2;4);B(-3;-1) v C(-2;1) . Chng minh 3

im A, B, C khng thng hng.

3) Rt gn biu thc: M = 1

x

x +

2x x

x x

vi x> 0 v x 1

Bi 3: (1.5im) Hai bn sng cch nhau 15 km. Th gian mt ca n xui dng t bn A n

bn B, ti bn B ngh 20 pht ri ngc dng t bn B tr v bn A tng cng l 3 gi. T nh

vn tc ca ca n khi nc yn lng, bit vn tc ca dng nc l 3 km/h.

Bi 4: (3.5 im) Cho na ng trn tm O ng k nh AB. Mt im C c nh thuc on

thng AO ( C khc A v C khc O ). ng thng i qua im C v vung gc vi AO ct

na ng trn cho ti D. Trn cung BD ly im M ( vi M khc B v M khc D). Tip

tuyn ca na ng trn cho ti M ct ng thng CD ti E. Gi F l giao im ca AM

v CD.

1. Chng minh : BCFM l t gic ni tip ng trn.

2. Chng minh EM = EF

3. Gi I l tm ng trn ngoi tip tam gic FDM. Chng minh D, I, B thng hng; t

suy ra gc ABI c s o khng i khi M thay i trn cung BD.

Bi 5:(1.0 im) Cho phng trnh ( n x ) : x2 (2m + 3)x + m = 0. Gi x1 v x2 l hai

nghim ca phng trnh cho. Tm gi tr ca m biu thc x12 + x2

2 c gi tr nh nht.

-------- HT ---------

CHNH THC


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S GIO DC V O TO THI TUYN SINH VO LP 10 THPT

QUNG TR Kha ngy 27 thng 6 nm 2011

MN: TON

Thi gian: 120 pht (khng k thi gian giao )

Cu 1 (2,0 im) Rt gn cc biu thc (khng s dng my t nh cm tay):

a) 27 5 12 2 3M ;

b) 1 1

:42 2

aN

aa a

, vi a > 0 v 4a .

Cu 2 (1,5 im) Gii cc phng trnh (khng s dng my t nh cm tay):

a) 2 5 4 0x x ;

b) 1 1

23

x

x

.

Cu 3 (1,0 im) c) V th (d) ca hm s y = -x + 3; d) Tm trn (d) im c honh v tung bng nhau.

Cu 4 (1,0 im) Gi x1, x2 l hai nghim ca phng trnh x

2 + 3x -5 = 0. T nh gi tr ca biu thc

2 2

1 2x x .

Cu 5 (1,5 im) Gii bi ton bng cch lp h phng trnh: T nh chu vi ca mt hnh ch nht, bit rng nu tng mi chiu ca hnh ch nht thm 4m th din t ch ca hnh ch nht tng thm 80m2 ; nu gim chiu rng 2m v tng chiu di 5m th din t ch hnh ch nht bng din t ch ban u. Cu 6 (3,0 im) Cho t gic ABCD ni tip na ng trn (O) ng k nh AD. Hai ng cho AC v BD ct nhau ti E. K vung gc vi AD (FAD; F O).

d) Chng minh: T gic ABEF ni tip c; e) Chng minh: Tia CA l tia phn gic ca gc BCF; f) Gi M l trung im ca DE. Chng minh: CM.DB = DF.DO.

--------------------HT-------------------

CHNH THC


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S GD&T BNH DNG

-------***-------

TUYN SINH VO LP 10 THPT NM HC 2011-2012 Mn : TON

Thi gian: 120 pht (khng k thi gian pht )

Bi 1: (1)

Tnh 215 8 15 16M x x , ti x= 15

Bi 2 (2) 1) V th hm s sau trn cng 1 mt phng to : y = 2x 4 (d) ; y = -x + 5 (d) V tm to giao im A ca (d) v (d) bng cch gii h phng trnh. 2) Tm m (P): y = mx2 i qua im c to (3;2)

Bi 3(2) 1) Gii phng trnh : x2 + 7x + 10 = 0 2) Gii phng trnh : x4 - 13x2 + 36 = 0

Bi 4(2) 1) T nh chiu di v chiu rng ca mt hnh ch nht c na chu vi l 33m v din t ch l

252m2 .

2) Cho phng trnh : x2 2(m + 2)x + 2m + 3 = 0 (1) Tm tt c gi tr m phng trnh (1) c 2 nghim phn bit u ln hn 0,5 .

Bi 5 (3) Cho ng trn (C) tm O. T 1 im A ngoi (C) v 2 tip tuyn AB, AC vi (C) (B,C l 2 tip im). V ng thng (d) qua C v vung gc vi AB, (d) ct ng thng AB ti H. ct (C) ti E, C v ct ng thng OA ti D.

1) Chng minh rng CH // OB v tam gic OCD cn . 2) Chng minh rng t gic OBDC l hnh thoi . 3) M l trung im ca EC, tip tuyn ca (C) ti E ct ng thng AC ti K. chng minh

O, M, K thng hng .

----Ht----


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S GIO DC O TO

NAM NH

THI TUYN SINH VO LP 10 THPT NM 2011 Mn: TON

CHNH THC Thi gian lm bi: 120 pht (khng k thi gian giao ). thi gm 01 trang

PHN 1 Trc nghim (2im):

Cu 1: Rt gn biu thc 8 2 c kt qa l

A. 10 B. 16 C. 2 2 D.3 2 .

Cu 2:Phng trnh no sau y c hai nghim tri du:

A. 2x x 0 B. 2x 1 0 C. 2x 1 0 D. 2x 2x 5 0

Cu 3: ng thng 2y mx m ct ng thng y = x + 1 ti im c honh bng 1 khi v

ch khi A.m = 1 B. m = - 2 C.m =2 D.m = 1 hoc m = -2

Cu 4: Hm s y m 1 x 2012 ng bin trn khi v ch khi

A. m B. m > 1 C. m < 1 D. m 1. Cu 5: Phng trnh 2x 1 . x 3 0 c tp nghim l

A. 1;3 B. 1;1 C. 3 D. 1;1;3 . Cu 6: Cho ng trn (O;R) c chu vi 4 cm . Khi hnh trn (O;R) c din t ch bng

A. 24 cm B. 23 cm C. 22 cm D. 2cm .

Cu7: Bit 3

sin5

, khi cos bng

A.2

5 B.

3

5 C.

4

5 D.

5

3.

Cu 8: Mt hnh tr c chiu cao bng 3cm, bn k nh y bng 4cm. Khi din t ch mt xung quanh ca hnh tr bng

A. 212 cm B. 224 cm C. 240 cm D. 248 cm .

PHN 2 T lun (9im):

Cu 1.(1,5 im): Cho biu thc : 2x x x x

Px x 1 x 1

(vi x 0 v x 1 )

1) Rt gn biu thc P. 2) Tm x bit P = 0.

Cu 2.(1,5 im): Cho phng trnh 2x x 2m 0 (vi m l tham s) 1) Gii phng trnh vi m = 1.

2) Tm m phng trnh trn c hai nghim phn bit 1 2x ; x tha mn 2

1 1 2x x x 2 .

Cu 3.(1,0 im): Gii h phng trnh:

1 14

x y

x(1 4y) y 2

Cu 4.(3,0 im): Cho na ng trn (O)ng k nh AB. im C thuc na ng trn (O) ( CB < CA, C khc B ). Gi D l im ch nh gia ca cung AC, E l giao im ca AD v BC.

1) Chng minh tam gic ABE cn ti B. 2) Gi F l im thuc ng thng AC sao cho C l trung im AF. Chng minh

EFA EBD.


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3) Gi H l giao im ca AC v BD, EH ct AB ti K, KC ct on EF ti I. Chng minh rng:

a) T gic EIBK ni tip

b) HF EI EK

BC BI BK .

Cu 5.(1,0 im): Gii phng trnh : 3 2x 3x 2 3 2x x x x 1 HT


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S GIO DC O TO NAM NH

THI TUYN SINH LP 10 TRNG THPT CHUYN NM HC 2011 2012 Mn: TON ( chung)

CHNH THC Thi gian lm bi: 120 pht

thi gm 02 trang

PHN 1 Trc nghim (1im): Mi cu sau c nu bn phng n tr li (A, B,C, D) , trong ch c mt phng n ng. Hy chn phng n ng v vit vo bi lm ch ci ng trc phng n la chn.

Cu 1: Phng trnh 2x mx m 1 0 c hai nghim phn bit khi v ch khi:

A. m 2 . B. m . C.m 2 . D. m 2 . Cu 2: Cho ng trn (O) ni tip tam gic MNP cn ti M. Gi E; F ln lt l tip im

ca ng trn (O) vi cc cnh MN; MP. Bit 0MNP 50 . Khi , cung nh EF ca ng trn (O) c s o bng:

A.0100 . B.

080 . C.050 . D.

0160 .

Cu 3: Gi l gc to bi ng thng y x 3 vi trc Ox, gi l gc to bi ng

thng y 3x 5 vi trc Ox. Trong cc pht biu sau,pht biu no sai ?

A.045 . B. 090 . C. 090 . D. .

Cu 4: Mt hnh tr c chiu cao l 6cm v din t ch xung quanh l 236 cm . Khi , hnh tr

cho c bn k nh y bng

A. 6 cm. B. 3 cm. C. 3 cm. D. 6cm.

PHN 2 T lun (9im):

Cu 1. (1,5 im) Cho biu thc : 3 x 1 1 1

P :x 1 x 1 x x

vi x 0 v x 1

3) Rt gn biu thc P. 4) Tm x 2P x = 3.

Cu 2.(2 im) 1) Trn mt phng vi h ta Oxy cho im M c honh bng 2 v M thuc th

hm s 2y 2x . Lp phng trnh ng thng i qua gc ta O v im M ( bit

ng thng OM l th hm s bc nht).

2) Cho phng trnh 2x 5x 1 0 1 . Bit phng trnh (1) c hai nghim 1 2x ;x . Lp phng trnh bc hai n y ( Vi cc h s l s nguyn ) c hai nghim ln lt l

1 2

1 2

1 1y 1 v y 1

x x

Cu 3.(1,0 im) Gii h phng trnh:

3 2 17

x 2 y 1 5

2x 2 y 2 26

x 2 y 1 5


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Cu 4.(3,0 im): Cho ng trn (O; R). Ly im M nm ngoi (O;R) sao cho qua M k c hai tip tuyn MA, MB ca (O;R) v gc AMB nhn ( vi A, B l cc tip im). K AH vung gc vi MB ti H. ng thng AH ct ng trn (O;R) ti N (khc A). ng trn ng k nh NA ct cc ng thng AB v MA theo th t ti I v K (khc A).

1) Chng minh t gic NHBI l t gic ni tip. 2) Chng minh tam gic NHI ng dng vi tam gic NIK. 3) Gi C l giao im ca NB v HI; gi D l giao im ca NA v KI. ng thng CD

ct MA ti E. Chng minh CI = EA.

Cu 5.(1,5 im)

1) Gii phng trnh : 22x x 9 x 9 22 x 1

2) Chng minh rng : Vi mi 2 3

2 3

1 1x 1, ta lun c 3 x 2 x

x x

.

----------------------------------------HT-----------------------------------------


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S GIO DC V O TO K THI TUYN SINH LP 10THPT THA THIN HU Kha ngy 24-6-2011 ------------ Mn :TON

CHNH THC Thi gian lm bi : 120 pht

Bi 1: (2,5 im )

a)Rt gn biu thc :A= 2

3 2 3

b) Trc cn mu s ri rt gn biu thc : B =2 3

243 2

c)Khng s dng my t nh cm tay, gii h phng trnh :

2x + 6y = 7

5x 2y = 9

Bi 2: (2,5 im)

Cho hm s y= 21

4x c th (P) v hm s y =mx 2 m 1 ( m 0) c th (d)

a)Trn cng mt mt phng ta , v th (P) v th (d) khi m=1. b)Tm iu kin ca m (P) v (d) ct nhau ti hai im phn bit c honh x1 v x2.

Khi xc nh m 2 21 2 1 2x x + x x = 48 .

Bi 3) (1 im) Trong mt phng c 144 ngi hp, c sp xp ngi ht trn dy gh (s ngi trn mi dy gh u bng nhau).Nu ngi ta thm vo phng hp 4 dy gh na, bt mi dy gh ban u 3 ngi v xp li ch ngi cho tt c cc dy gh sao cho s ngi trn mi dy gh u bng nhau th va ht cc dy gh.Hi ban u trong phng hp c bao nhiu dy gh ? Bi 4) (1,25 im) Cho tam gic ABC vung A (hnh bn)

a) T nh sin B.Suy ra s o ca gc B. b) T nh cc di HB,HC v AC.

4 cm

8 cm

H CB

A

Bi 5) (1,5 im ) Cho tam gic nhn ABC ni tip trong ng trn (O;R).V cc ng cao BD v CE (DAC,E AB) v gi H l trc tm ca tam gic ABC.V hnh bnh hnh BHCG a)Chng minh:T gic AEHD ni tip v im G thuc ng trn (O;R). b)Khi ng trn (O;R) c nh, hai im B,C c nh v A chy trn (O;R) th H chy trn ng no? Bi 6): (1,25 im) Cho hnh ch nht MNDC ni tip trong na ng trn tm O, ng k nh AB (M,N thuc on thng AB v C,D trn na ng trn.Khi cho na ng trn ng k nh AB v hnh ch nht MNDC quay mt vng quanh ng k nh AB c nh, ta c mt hnh tr t kh t vo trong hnh cu ng k nh AB. Bit hnh cu c tm O, bn k nh R=10 cm v hnh tr c bn k nh y r= 8 cm t kh t vo trong hnh cu .T nh th t ch hnh cu nm ngoi hnh tr cho.

Ht


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S gio dc -o to

H nam

chnh thc

K thi tuyn sinh vo lp 10 THPT chuYN

Nm hc 2011-2012

Mn : TON- chung Thi gian lm bi :120 pht (Khng k thi gian giao )

Thi chiu 22 thng 7 nm 2011

Bi 1: ( 2 ) 1/ Rt gn: P =6 1 5 1

:5 5 1 5 45

2/ Gii PT : 3 23 5 0x x x

Bi 2: (2 ) Cho hm s y = - 8x2 c th l (P)

a/ Tm to ca 2 im A, B trn th (P) c honh ln lt l -1 v 1

.2

b/ Vit phng trnh ng thng AB

Bi 3: (2 )

1/ Tm gi tr ca x tho mn:

1 1 1 499

...201216 17 68 17 18 18 17 1 ( 1)x x x x

2/ Cho x, y l cc s khng m tho mn : x+y = 4. Tm gi tr nh nht , gi tr ln nht

ca biu thc P = 4 4 3 3 2 2 2 25( ) 14 58 6x y xy x y x y x y xy

Bi 4 ( 4 )

Cho t gic ABCD ni tip ng trn (O) v AD l ng k nh. Gi I l im ch nh

gia ca cung nh BC; ng thng AI ct dy cung BC v ng thng DC ln lt ti E,M

; ng thng DI ct dy cung BC v ng thng AB ln lt ti F, N.

a / C/m hai tam gic IAN v IDM ng dng .

b / C/m t gic ANMD l t gic ni tip.

c / C/m ng thc: IE.IA = IF.ID

d / C/m OI vung gc vi MN

Ht

H v tn th sinh: .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..S bo danh.... .. .. .. .. .. .. .. .. .. .. .. .. .. Ch k ca gim th 1.. .. .. .. .. .. .. .. .. .. .. . .. .. ..Ch k ca gim th 2.. .. .. .. .. .. .. .. .. .. .. ..


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