Loi Giai de Thi Vao Lop 10 Nam Hoc 2012 2013 Cua Hanoi

7/31/2019 Loi Giai de Thi Vao Lop 10 Nam Hoc 2012 2013 Cua Hanoi

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S GD&T THNH PH H NI THI TUYN SINH VO LP 10Mn thi : Ton

Nm hoc: 2012 2013Ngy thi : 21 thng 6 nm 2012

Thi gian lm bi: 120 phtBi I (2,5 im)

1) Cho biu thc4

2

xA

x

+=

+Tnh gi tr ca biu thc A khi x = 36.

2) Rt gn biu thc4 16

:4 4 2

x xB

x x x

+= + + +

(vi x 0, x 16).

3) Vi cc biu thc A v B ni trn, hy tm cc gi tr nguyn ca x gi tr ca biu thB(A 1) l s nguyn.

Bi II (2,0 im) Gii bi ton sau bng cch lp phng trnh hoc h phng trnh:

Hai ngi cng lm chung mt cng vic trong12

5gi th xong. Nu mi ngi lm mt mn

th thi gian ngi th nht hon thnh cng vic t hn ngi th hai l 2 gi. Hi nu lm m

mnh th mi ngi phi lm trong bao nhiu gi xong cng vic?Bi III (1,5 im)

1) Gii h phng trnh

2 12

6 21

x y

x y

+ = =

2) Cho phng trnh : 2 2(4 1) 3 2 0x m x m m + = (n x). Tm m phng trnh c h

nghim phn bit x1,x2 tha mn iu kin2 2

1 2 7x x+ =Bi IV (3,5 im)

Cho ng trn (O; R) ng knh AB. Bn knh CO vung gc vi AB, M l im bt k trcung nh AC (M khc A v C), BM ct AC ti H. Gi K l hnh chiu ca H trn AB.1) Chng minh t gic CBKH l t gic ni tip.2) Chng minh ACM ACK=

3) Trn on thng BM ly im E sao cho BE = AM. Chng minh tam gic ECM l tam givung cn ti C.

4) Gi d l tip tuyn ca ng trn (O) ti im A. Cho P l mt im nm trn d sao cho ha

im P, C nm trong cng mt na mt phng b AB v.AP MB

RMA

= . Chng minh n

thng PB i qua trung im ca on thng HK.

Bi V(0,5 im) Vi x, y l cc s dng tha mn iu kin x

2y, tm gi tr nh nht ca biu thM =

2 2x y

xy

+.

........................................ Ht........................................Lu :Gim th khng gii thch g thm.H tn th sinh:............................................................ S bo danh:...............................Ch k gim th 1: Ch k gim th 2:

CHNH THC


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P AN - THANG IM (Tham Khao)Cu Ni dung

Bi I(2,5 )

1) Vi x = 36, ta c : A =36 4 10 5

8 436 2

+= =

+

0,75

2) Vi x , x 16 ta c :

B =x( x 4) 4( x 4) x 2

x 16 x 16 x 16

+ ++

+ =

(x 16)( x 2) x 2

(x 16)(x 16) x 16

+ + +=

+

1,25

3) Biu thc B (A 1) =x 2 x 4 x 2

x 16 x 2

+ + +

=2

x 16l s nguyn

x 16 = 1 hay x 16 = 2 x = 15 hay x = 17 hay x = 14 hay x = 18

0,25

0,25

Bi II

(2,0)

Gi s gi ngi th nht hon thnh cng vic mt mnh l x (gi) ,k x > 12/5s gi ngi th hai hon thnh cng vic mt mnh l x + 2 gi

0,5

Trong 1 gi : ngi th nht lm c : 1/x cng vicNgi th 2 lm c : 1/ x + 2 cng vic

0,25

Ta c phng trnh :

1 1 5

x x 2 12+ =+

0,5

Gii phng trnh : x = 4 tha mn k ca n 0,5Vy ngi th nht lm xong cng vic trong 4 gi vngi th hai lm xong cng vic trong 6 gi

0,25

Bi III(1,5 )

1)

2 12

x y

6 21

x y

+ = =

2 12

x y

55 [pt(2) 3pt(1)]

y

+ = =

y 1

21

x

=

=

x 2

y 1

=

=0,75

2) = (4m 1)2 12m2 + 8m = 4m2 + 1 > 0, m

Vy phng trnh c 2 nghim phn bit m

0,25

Ta c : x1 + x2 =b

a = 4m 1 v x1.x2 =

c

a= 3m2 2m

0,25

Do , theo bi ra ta c (x1 + x2)2 2x1x2 = 7 (4m 1)2 2(3m2 2m) = 7 10m2 4m 6 = 0

m = 1 hay m =3

5

0,25

Bi IV(3,5 )

1) T gic CBKH c hai gc i 090HCB HKB= =khng nh t gic CBKH ni tip trong ng trn ng knh HB.

0,50,5

2) Gc ACM ABM= chn cung AMv ACK HCK HBK= = v cng chn cung HK.

Vy ACM ACK=

0,250,50,25


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S GIO DC V O TO K THI TUYN SINH LP 10 THPTTP.HCM Nm hoc: 2012 2013

CHNH THC MN: TONThi gian lm bi: 120 pht

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

a) 22 3 0 =x x

b)

2 3 7

3 2 4

=

+ =

x y

x yc) 4 2 12 0+ =x xd) 2 2 2 7 0 =x x

Bi 2: (1,5 im)

a) V th (P) ca hm s 21

4=y x v ng thng (D):

12

2= +y x trn cng mt h trc to

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

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

1 2 1

1= +

+

xA

xx x x xvi x > 0; 1x

(2 3) 26 15 3 (2 3) 26 15 3= + + BBi 4: (1,5 im)

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

Tm m biu thc M = 2 21 2 1 2

24

6

+ x x x x t gi tr nh nht

Bi 5: (3,5 im)Cho ng trn (O) c tm O v im M nm ngoi ng trn (O). ng thng MO ct (Oti E v F (ME


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

a) 22 3 0 =x x (a)V phng trnh (a) c a - b + c = 0 nn

(a)3

12

= =x hay x

b)2 3 7 (1)

3 2 4 (2)

= + =

x y

x y

2 3 7 (1)

5 3 (3) ((2) (1) )

=

+ =

x y

x y

13 13 ((1) 2(3))

5 3 (3) ((2) (1) )

=

+ =

y

x y

1

2

= =

y

x

c) 4 2 12 0+ =x x (C)t u = x2 0, phng trnh thnh : u2 + u 12 = 0 (*)

(*) c = 49 nn (*) 1 7

32

+= =u hay

1 74

2

= = u (loi)

Do , (C) x2 = 3 x = 3Cch khc : (C) (x2 3)(x2 + 4) = 0 x2 = 3 x = 3

d) 2 2 2 7 0 =x x (d) = 2 + 7 = 9 do (d) x = 2 3

Bi 2:a) th:

Lu : (P) i qua O(0;0), ( ) ( )2;1 , 4; 4

(D) i qua ( ) ( )4;4 , 2;1b) PT honh giao im ca (P) v (D) l

21 1 24 2

= +x x x2 + 2x 8 = 0 4 2 = =x hay x

y(-4) = 4, y(2) = 1Vy to giao im ca (P) v (D) l ( ) ( )4;4 , 2;1 .

Bi 3:Thu gn cc biu thc sau:1 2 1

1= +

+

xA

xx x x x

2

2

1

= +

x x x x x

x x x


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2 2

( 1) 1

= +

x x

x x x

2 11

1

= +

x

x x 2 ( 1)

( 1)

=

x x

x x

2=

xvi x > 0; 1x

(2 3) 26 15 3 (2 3) 26 15 3= + + B1 1

(2 3) 52 30 3 (2 3) 52 30 32 2

= + +

2 21 1(2 3) (3 3 5) (2 3) (3 3 5)2 2

= + +

1 1(2 3)(3 3 5) (2 3)(3 3 5) 22 2

= + + =

Cu 4:a/ Phng trnh (1) c = m2 - 4m +8 = (m - 2)2 +4 > 0 vi mi m nn phng trnh (1) c 2 nghim phn bit vi mm.

b/ Do , theo Viet, vi mi m, ta c: S = 2b

ma

= ; P = 2= c

ma

M = 21 2 1 2

24

( ) 8

+ x x x x

=2 2

24 6

4 8 16 2 4

=

+ +m m m m

26

( 1) 3= +m

. Khi m = 1 ta c 2( 1) 3 +m nh nht

2

6

( 1) 3 =

+M

mln nht khi m = 1 2

6

( 1) 3

=

+M

mnh nht khi m = 1

Vy M t gi tr nh nht l - 2 khi m = 1

Cu 5

a) V ta c do hai tam gic ng dng MAE v MBF

NnMA MF

ME MB= MA.MB = ME.MF (Phng tch ca M i vi ng trn tm O)

b) Do h thc lng trong ng trn ta c MA.MB = MC2, mt khc h thc lng trong tam givung MCO ta c MH.MO = MC2 MA.MB = MH.MO nn t gic AHOB ni tip tronng trn.

c) Xt t gic MKSC ni tip trong ng trn ng knh MS (c hai gc K v C vung).Vy tc : MK2 = ME.MF = MC2 nn MK = MC. Do MF chnh l ng trung trc ca KC nMS vung gc vi KC ti V.

d) Do h thc lng trong ng trn ta c MA.MB = MV.MS ca ng trn tm Q.Tng t vi ng trn tm P ta cng c MV.MS = ME.MF nn PQ vung gc vi MS v lng trung trc ca VS (ng ni hai tm ca hai ng trn). Nn PQ cng i qua trunim ca KS (do nh l trung bnh ca tam gic SKV). Vy 3 im T, Q, P thng hng.

M E F

K

SA

BT

P

Q

C

H O

V


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Loi Giai de Thi Vao Lop 10 Nam Hoc 2012 2013 Cua Hanoi