Ti liu thi vo lp 10 Gv : Lu vn Chung 1 www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 2 THAM KHO THI TUYN SINH VO LP 10 Bi 1( 1,5 im ) Gii ccphng trnh v h phng trnh sau :a)x4 8x2 + 15 = 0b)11 6 405 7 11 =+ = x yx y c) x2 2( 3 1 )x 4 3= 0 Bi 2( 1,5 im ) Tnh v rt gn cc biu thc sau :a)A =+ ( 5 3). 7 - 3 5b)B = a 2 a b 1 1:a ab b ab a b| | | ||| | \ .\ .+ ( vi a > 0; b > 0 ; a=b) Bi 3( 2 im ) Trong cng mt phng ta Oxy cho (P): y = 24x v (d) : y = 122 + xa)V (P) v (d) trn cng mt phng ta b)Tm ta giao im ca (P) v (d) bng php ton c)Tm phng trnh ng thng (D) tip xc vi (P) song song vi ng thng (d) Bi 4 ( 1,5 im ) Cho phng trnh bc hai : x2 2(m 3)x 2m 1 = 0( m l tham s ) a)Chng tphng trnh c hai nghim phn bit x1 ; x2 vi mi gi tr m b)Tm gi tr m phng trnh c hai nghim tha mn : x12 + x22 = 14 c)Tm gi tr nh nht ca biu thc A = x12 + x22 x1.x2v gi tr m tng ng. Bi 5 ( 3,5 im) Cho tam gic ABC c ba gc nhn ni tip ng trn (O) vi AB < AC . Hai ng cao BE v CF ct nhau ti H. a)Chng minh AH vung gc vi BC v t gic BFEC ni tip ng trnb)ng thng EF ct ng thng BC ti M. Tia AM ct ng trn (O) ti K. Chng minh ME.MF = MK.MA c)Chng minh HK vung gc vi AM d)Gi I l trung im BC. Chng minh ba im H , I , K thng hng . 1www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 3 THAM KHO THI TUYN SINH VO LP 10 Bi 1( 1,5 im ) Gii ccphng trnh v h phng trnh sau :a) 4x4 21x2 + 20 = 0b) 3x - 4y = 58x -9y =10c)x2 (3 5 )x 3 5= 0 Bi 2( 1,5 im ) Tnh v rt gn cc biu thc sau :A=3 8- 151+ -230 - 2 B =( ) ( )10 + 2 3+ 5 6- 2 5 Bi 3( 2 im ) Trong cng mt phng ta Oxy cho (P): y = 24x v (dm) : y = x + ma)V (P) v (d) trn cng mt mt phng ta khi m =3 b)Tm m (dm) tip xc vi (P). Tm ta tip imc)Tm m (dm) ct (P) ti hai im phn bit A v B sao cho xA2 + xB2 = 10 Bi 4( 1,5 im ) Chophng trnh bc hai : x2 + 2(m 1)x + m2 + 5 = 0( m l tham s )a)Tm iu kin ca m phng trnh lun c hai nghim x1 ; x2

b)Tm m phng trnh c hai nghim tha mn : 1 22 1x x+ = 2x x Bi 5( 3,5 im ) T im A ngoi ng trn (O) v hai tip tuyn AB v AC(B v C l hai tip im ) v ct tuyn AEF vi ng trn ( EB < EC , E nm gia A v F) a)Chng minh OA vung gc vi BC ti H v t gic ABOC ni tipb)Chng minh : AE.AF = AH.AO c)Gi K l trung im EF. V dy ED OB ct BC ti M , ct FB ti N.Chng minh t gic KMEC ni tipd)Chng minh tia FM i qua trung im AB. 2www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 4

THAM KHO THI TUYN SINH VO LP 10 Bi 1 Cho biu thc A = 2 1 21 :11 1| | | | || ||\ . \ . ++ + ++x xxx x x x x a)Tm iu kin c ngha ca biu thc A b)Rt gn A c)Tnh gi tr A khi x =2009 8032 Bi 2 Gii ccphng trnh v h phng trnh sau : a) x4 6x2 16 = 0b) 12 5 77 4 11 =+ =x yx yc)x2 2|x| 3 = 0 d) x 2y 3xy 5 == Bi 3 Trong mt phng ta Oxy cho (P): y = x2 v ng thng (dm): y = mx + m 1a)V (P) v (d) khi m = 3 b)Tm m (P) v (dm) tip xc . Tm ta tip imc)Vitphng trnh ng thng (D) tip xc vi (P) v i qua im A(0 ; 1) Bi 4 Chophng trnh bc hai : mx2 (m 1)x 2m + 1 = 0 ( m l tham s ) a)Tm iu kin ca m phng trnh c hai nghim phn bit x1 ; x2

b)Tm h thc gia x1 v x2 khng ph thuc vo m ( m=0) c)Tm m phng trnh c hai nghim x1 ; x2 sao cho x12 + x22 t gi tr nh nht Bi 5 Cho tam gic ABC c ba gc nhn ni tip ng trn (O) v AB < AC. Ba ng cao AD , BE , CF ct nhau ti H. Gi I l trung im BC. a)Chng minh cc t gic BFEC v AFHE ni tipb)Tia IH ct (O) ti N. Chng minhAANH vung ti N c)EF ct BC ti M. Chng minh t gic NFBM ni tipd)Chng minh A , N , M thng hng 3www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 5 THAM KHO THI TUYN SINH VO LP 10 Bi 1 Gii ccphng trnh v h phng trnh sau : a) 4x4 36x2 = 0 b) 13 8 36 5 16 =+ = x yx y d) x2 22x 1 + 7 = 0 Bi 2 1)Tnh gi tr ca biu thc :3 5 3 53 5 3 5 +++ 2)Cho A = xx 2 x 1 x 1:2x x 1 x x 1 1| | | |\ .+ + + + + vi x > 0;x=1a) Rt gn A b)Chng minh A>0c)Tm x A = 89 Bi 3 Trn cng mt phng Oxy cho (P): y = 21x2v(d): y = 2x + m + 1a)Tm m (d) i qua im A thuc (P) v c honh bng 2 b)Tm m (d) tip xc vi (P).Tm ta tip imc)Tm m (d) ct (P) ti hai im phn bit c honh x1 ; x2 sao cho 2 21 21 1 1x x 2+ = Bi 4 Chophng trnh bc hai : x2 + (m 3)x 2m + 2 = 0( m l tham s ) a) Chng t phng trnh lun c hai nghim x1 ; x2 vi mi gi tr m b) Tm m phng trnh c hai nghim tri du c) Tm m phng trnh c hai nghim tha mn : (x1 x2 )2 = 4d) Tm m phng trnh c hai nghim tha mn : 2x1 + x2 = 3 Bi 5 Cho ng trn (O;R) ng knh BC. Ly im M ty thuc bn knh OC. Qua M v dy AE vung gc vi BC. T A v tip tuyn ca (O) ct ng thng BC ti D a)Chng minh EC l phn gic ca gc AED b)V ng cao AK caABAE. Gi I l trung im AK.Tia BI ct ng trn (O) ti H. Chng minh MH vung gc vi AH c)Chng minh t gic EMHD ni tipd)Chng minh ng thng BD tip xc vi ng trn (AHD) 4www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 6

THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a) 2x4 5x2 +2 = 0b) 7 4 59 10 14 =+ =x yx yd) x

x 3 9 = 0 Bi 2 1)Tnh gi tr ca biu thc : 2 3 2 3 + 2)Cho biu thc : A = 1 1 x xx 1xx 1 x x 1 x+ + + a) Rt gn Ab)Tnh gi tr ca A khi x = 539 2 7 c) Tm x A = 16 Bi 3 Trn cng mt phng Oxy cho (P): y = 241x v(d): y = 1x 22a)V (P) v (d) trn cng mt phng ta v tm ta giao im bng php ton b)Vitphng trnh ng thng (D) tip xc vi (P) v vung gc vi (d) c)Vitphng trnh ng thng (D) i qua M( 1 ; 1) v tip xc vi (P) Bi 4 Chophng trnh bc hai : x2 + 2(m 1)x 2m + 5 = 0( m l tham s ) a)Tm iu kin ca m phng trnh c nghimb)Tm m phng trnh c hai nghim x1 ; x2tha mn : x1 + 2x2 = 9c)Tm m phng trnh c hai nghim x1 ; x2 sao cho A = 12 10x1x2+ x12 + x22

t gi tr nh nht Bi 5 Cho na ng trn (O) ng knh AB v im C trn na ng trn(CA > CB). K CH vung gc vi AB ti H. ng trn tm K ng knh CH ct AC ti D v BC ti E, ct na ng trn (O) ti im th hai l F. a)Chng minh CH = DE v CA.CD = CB.CE b)Chng minh t gic ABED ni tipc)CF ct AB ti Q . Hi K l im c bit g ca tam gic OCQ d)Chng t Q l mt giao im ca DE v ng trn ngoi tipAOKF 5www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 7 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a)9x4 10x2 + 1 = 0b)12x + 7y = 227x + 13y = -5 c) 15 17 = x x Bi 2 Chophng trnh bc hai : x2 2(m + 4)x + m2 8 = 0( m l tham s ) a)Tm iu kin ca m phng trnh c hai nghim x1 ; x2

b)Tm m biu thc A = x1 + x2 3x1x2t gi tr ln nhtc)Tm m biu thc B = x12 +x22 x1x2 t gi tr nh nhtd)Tm h thc lin h gia x1 v x2 khng ph thuc vo m Bi 31) Tnh gi tr biu thc : 32( 2 6)3 2++ 2) Cho biu thc M = x x 1 x x 1 1 x 1 x 1xx x x x x x 1 x 1| | | || | || | ||\ .\ . \ . + + + + + + ( x > 0 ; x=1) a) Rt gn biu thc M b)Tm x M = 7 Bi 4Trong mt phng Oxy cho Parabol (P) : y = 2 x4 v im A( 1 ; 2 ) a)Vitphng trnh ng thng (d) i qua A v c h s gc lm b)Chng t (P) v (d) lun ct nhau ti hai im phn bitc)Tm m (d) ct (P) ti hai im c honh x1 ; x2 sao cho x12.x2 + x22.x1 t gi tr nh nht . Tm gi tr nh nht ? Bi 5 Cho ng trn (O) ng knh AC v im B thuc on OC. Gi M l trung im AB. V dy DE vung gc vi AB ti M. K BF vung gc vi DC ti F. a)Chng minh t gic ADBE l hnh thoi v t gic DMBF ni tipb)Chng minh CF.CD = CB.CMc)Chng minh ba im B , E , F thng hng vEB.EF = 12ED2 d)Gi S l giao im ca BD v MF , CS ct DA ti H v ct DE ti K. Chng minh h thc : DA DB DEDH DS DK+ = 6www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 8 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a)4x4 7x2 + 3 = 0 b)10x + 9y = 87x + 6y = 5 c)(x 1)(x 2)(x 3)(x 4) = 24 Bi 21) Tnh gi tr biu thc : 1 3 4A11 2 30 7 40 8 4 3= + 2) Cho biu thc K = 3x 9x 3 x 1 x 2x x 2 x 2 1 x+ + ++ + ( x > 0 ;; x =1 ) a)Rt gn biu thc K b)Tnh K khi x = 3 +2 2 c) Tm x nguyn dng K nhn gi tr nguyn Bi 3Chophng trnh bc hai : x2 mx 7m + 2= 0 ( m l tham s ) a)Tm m phng trnh c mt nghim x = 2. Tm nghim cn li. b)Tm m phng trnh c hai nghim tri du. c)Tm m phng trnh c hai nghim x1 ; x2 tha mn : 2x1 + 3 x2 = 0d)Tm m phng trnh c hai nghim sao cho biu thc A = 1 21 2x xx x 1 + nhn gi tr nguyn Bi 4 Trong mt phng Oxy cho (P) : y =22x v ng thng (d) : y = 2x 2a)Chng minh (P) v (d) tip xc nhau . Tm ta tip imb)Tm m ng thng (dm): y = 3mx 2 lun ct (P) ti 2 im phn bit c)Tm nhng im thuc (P) v cch u hai trc ta Bi 5Cho ng trn (O) v dy BC. Mt im A thuc cung ln BC ( AB < AC).Tip tuyn ti A ct BC ti M. Phn gic ca BACct BC ti E v ct (O) ti D. OD ct BC ti K.a)Chng minh t gic MAOK ni tipvME = MA b)V tip tuyn th hai MF vi (O). Chng minh FE l phn gic ca BFC c)Gi I l tm ng trn ngoi tipAAEC . Chng minh ba ng thng FE , DO v CI ng quyd)Cho BE = 2 ; CE = 3 . Tnh MA . 7www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 9 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a)4x4 5x2 + 1 = 0 b)4x - 9y = 922x + 6y = 31c)(2x 1)4 + 7(1 2x)2 = 8Bi 2Rt gn cc biu thc sau : A = 30 2. 214 80 66 1 6 2| | |\ .++ B =3 5 3 510 3 5 10 3 5+ + + + Bi 3Rt gn v tnh gi tr biu thc M khi x =3 5 +M =1x 1 2x x x 1 2x x: 12x 1 2x 1 2x 1 2x 1| | | | || ||\ . \ .+ + + ++ ++ + ( x> 0 ; x 12=) Bi 4Chophng trnh bc hai : (m + 1)x2 2(m 1)x + m 2= 0 ( m l tham s ) a)Tm iu kin ca m phng trnh c hai nghim phn bit b)Tm m phng trnh c hai nghim x1 ; x2 sao cho1 21 1 7x x 4+ =Bi 5 Trong mt phng Oxy cho (P) : y = ax2v im A( 2 ; 1 ) a)Xc nh a v v (P) bit (P) i qua im A b)Cho im B e (P) v c xB = 4 . Vitphng trnh ng thng AB c)Vitphng trnh ng thng (d) tip xc vi (P) v song song vi AB Bi 6 Cho tam gic ABC c ba gc nhn ni tip ng trn (O;R) (AB < AC). Phn gic ca gc BAC ct BC ti D v ct ng trn (O) ti M. Tip tuyn ti A ca (O) ct BC ti S. a)Chng minh OM vung gc vi BC ti I v SA = SD b)V ng knh MN ca (O) ct AC ti F, BN ct AM ti E. Chng minh EF // BC c)V tip tuyn SK ca (O) (K l tip im, K=A).Chng minh K, N, D thng hngd)Cho AB = 4 ; BC = 5 ; AC = 6 . Chng minh tam gic SAB cn 8www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 10 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a) 4x2 4x 5+ 1 = 0 b)5x 2y 174x 3y 1+ = + = c)5x4 3(x2 + 1) = 7x2 3Bi 2Rt gn cc biu thc sau : A = 2 8 12 5 2718 48 30 162 + +B = 3 5(3 5)10 2 ++ C = 2a a 8 a 42 a .a 2 a 2| | | | || | \ .\ .+ + ( a> 0 ; a4 =) D = x 5 x 25 x x 3 x 51 :x 25x 2 x 15 x 5 x 3| | | | || ||\ . \ . + ++ + ( x> 0 ; x =25 ; x=9) Bi 3Chophng trnh bc hai : x2 2(m + 1)x + m2 3m + 2= 0 ( m l tham s ) a)Tm iu kin ca m phng trnh c hai nghim phn bit x1 ; x2

b)Tm m phng trnh c hai nghim tha mn : x12 + x22 = 16c)Tm m phng trnh c hai nghim sao cho biu thc : M = (x1 + x2)2 5x1.x2t gi tr ln nht Bi 4 Trong mt phng Oxy cho (P) : y =22x v ng thng (d) : y = mx+ m 4a)Xc nh m (P) v (d) tip xc . Xc nh ta tip imb)Vitphng trnh ng thng (d) tip xc vi (P) v i qua im A(0 ; 2 ) Bi 5 Cho ng trn (O;R) ng knh AB. Cl im chnh gia cung AB. M l im thuc cung nh BC. V tia Cx vung gc vi AM ti N ct AB ti E. a)Chng minh t gic AONC ni tipb)AM ct BC ti K. Chng minh t gic ONKB ni tipc)Chng minh OA.NE = OE.NA d)Tnh din tch t gic AEMC theo R e)Chng minh AN = MN + MB f)Khi K l trung im BC. Chng minh AN = 2MN 9www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 11 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a)x2 2(3 2 2 )x + 17 12 2= 0 c)x2 2x 2 |x 1 | 2 = 0 b) 5(x 2y) 3(x y) 99x y 7(x y) 3y 17+ = = + d) x y 1 0x(y 1) 9 ++ =+ = Bi 2 Rt gn cc biu thc sau : A =2 4 6 2 5 ( 10 2)| | |\ .+ B = 3 5 3 510 3 5 10 3 5+ + + + C = 1 1 1 1...1 2 2 3 3 4 2008 2009+ + + ++ + + + Bi 3Cho biu thc M= 1 x x 1 x 1 x x 4:x 1 x x 2 x 2 x x 2| | | | || ||\ . \ . + + + + + + ( x> 0 ; x=1) a) Rt gn Mb) Tm x M = 2 x 1 +c) Tm gi tr nh nht ca M Bi 4Chophng trnh bc hai : x2 mx + m 1= 0 ( m l tham s ) a)Chng tphng trnh lun c 2 nghimx1 ; x2 vi mi gi tr m b)Tm gi tr m x12x2 + x22x1= 2 c)Tm gi tr nh nht ca biu thc A = x12 + x22 6x1x2v gi tr m tng ng d)Tm h thc gia x1 v x2 khng ph thuc vo gi tr m Bi 5Trong mt phng Oxy cho (P) : y =24xv ng thng (d) : y = mx 2m 1a) V (P) b) Tm m (P) v (d) tip xc .Tm ta tip im . c) Tm m (d) ct (P) ti hai im phn bit AB sao cho on AB ct trc tung Bi 6 Cho ng trn (O;R) ng knh AB , C l im bt k trn (O) khc A v B. tip tuyn ti A ct ng thng BC ti N. Gi M l trung im BC. a)Chng minh t gic AOMI ni tipb)K dy AK vung gc vi ON ti H. Chng minh t gic ANKM ni tipc)Chng minh hai ng thng CO , KM v ng thng qua A song song vi BC ct nhau ti im thuc ng trn (O) d)Chng minh HK l tia phn gic ca gc CHB e)Gi E l giao im ca tia AK v tia OM. Chng minh EB l tip tuyn ca (O;R) 10www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 12 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a) x2 ( 5 1 )x 5= 0 b)3x 4y 255x 7y 43 = =c)x2(x + 1)2 x(x + 1) 30 = 0 Bi 2 Rt gn cc biu thc sau : a)A =227 30 2 123 22 2 + + b) B = 2 3 22 3 6 8 4+ ++ + + + Bi 3Cho biu thc M=x x 9 3 x 1 1:9 x3 x x 3 x x| | | | || ||\ . \ .+ ++ + a)Tm iu kin c ngha ca biu thc M b)Rt gn biu thc M v tm x nu M = 34Bi 4a) Chophng trnh bc hai : x2 2x + m = 0 ( m l tham s ) Tm m phng trnh c hai nghim phn bit x1 ; x2 sao cho 7x2 4x1 = 47 b) Tm gi tr k bit phng trnh :x2 (2 + k)x 3 k = 0 ( k l tham s )c tng bnh phng hai nghim bng 50. Bi 5Trong mt phng Oxy cho (P) : y =ax2v ng thng (d) : y = 2x a2( a> 0) a)Tm a (P) v (d) lun ct nhau ti hai im phn bit A v Bb)Chng minh nu (P) v (d) ct nhau ti hai im phn bit th on thng AB khng ct trc tung c)Gi xA vxB l honh ca A v B . Tm gi tr nh nht ca biu thc Q = A B A B4 1x x x .x++ Bi 6 Cho tam gic ABC c ba gc nhn ni tip ng trn (O;R). V ng cao AH ca tam gic ABC v ng knh AD ca ng trn (O). Gi E v F ln lt l hnh chiu ca C v B ln ng thng AD. Gi M l trung im BC a)Chng minh cc t gic ABHF v BMOF ni tipb)Chng minh EH song song vi DB c)Chng minh AB.AC = AH.AD d)Gi S l din tchAABC. Chng minh S = AB.AC.BC4R e)Chng minh M l tm ng trn ngoi tip tam gic EHF 11www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 13 THAM KHO THI TUYN SINH VO LP 10 Bi 1Gii cc phng trnh v h phng trnh sau : a)x4 44x2 1280 = 0b)(x 3)4 + 5(x 3)2 = 36c) 2 3 8 53 4 5 5 =+ = x yx y d)5 2 332 82+ = =x yx y e)2( 2)( 1) 360 + + = x x x x f) 2 2216 = =x yx y Bi 2 Rt gn cc biu thc sau : a) 2 3 2 32 2 3 2 2 3+ ++ + b)( 12 2 14 2 13 12 2 11)( 11 13) + + + + c)12 6 3. 3 33 3+d)( )3 1 4 4 a > 0 ; a 442 2+ + = +a a aaa a Bi 3Cho biu thc2 x x 1 x 2A ( ) :x x 1 x 1 x x 1| | | |\ .+ += + + a) Rt gn biu thc Ab) Tnh gi tr caAkhi x =4 2 3 + Bi 4 Tm m phng trnh : x2 (m + 1)x + 2m = 0(m l tham s)c hai nghim phn bit x1 ; x2 sao cho x1 v x2 l di hai cnh gc vung ca mt tam gic vung c cnh huyn bng 5 Bi 5 Mt hnh ch nht c chu vi 22m. Nu tng chiu di 3m v chiu rng thm 2 m th din tch tng thm 32 m2 . Tm kch thc hnh ch nht ban u ?Bi 6 Trong mt phng ta Oxy cho (P) : y = 12 x2v(d) : y = 2x ma)Tm m (P) v (d) tip xc . Tm ta tip im . b)Tm m (d) ct (P) ti hai im phn bit u nm bn tri trc tung. Bi 7 Cho tam gic ABC vung ti A ( AB < AC ). ng trn (O) ng knh AB v ng trn (I) ng knh AC ct nhau ti im th hai l D. a)Chng minh B , C , D thng hngb)Gi M l im chnh gia cung nh DC ca (I). IM ct DC ti F. Chng minh t gic BAIF ni tipc)AM ct BC ti E v ct ng trn ti N. Chng minhAABE l tam gic cn d)Gi K l trung im MN. Chng minh OK vung gc vi IK 12www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 14 THAM KHO THI TUYN SINH VO LP 10 Cu 1Gii cc phng trnh v h phng trnh sau: a) 6x2 x 1 = 0b) x4 6x2 27 = 0c) 5x 6y 78x 9y 10+ =+ =d) 2x 3 y 45x 2 y 29 =+ = d) 72 36 50 25 8 4 0 + = x x x x e)142 5 33 5 =+ xxx Cu 2a) V th (P) ca hm s y = 14x2 v ng thng (D): y = 12x 2 trncng mt cng mt h trc to . b) Tm to cc giao im ca (P) v (D) cu trn bng php tnh. c) Vit phng trnh ng thng tip xc vi (P) v ct trc tung ti im c tung bng 4 Cu 3 Thu gn cc biu thc sau: a)A = 58 3 7 8 3 714 3+ +

b) B = 9 9 663 3 + + x x xx x( x> 0va x=9 ) c) C = 1 x x x 1 x: xx 1 x 1x 1| | | | || ||\ . \ . + ( x > 0 ;x=1) Cu 4 Cho phng trnh : 2x2 2(m + 1)x + m 1 = 0 (m l tham s) a) Chng minh phng trnh trn lun c hai nghim x1 ; x2 vi mi gi tr m b) Tm m biu thcA = 2 21 2 1 2x x 6x x + t gi tr nh nht Cu 5 Cho ng trn (O;R) v dy BC = R 3 . A l im thuc cung ln BC . K ba ng cao AD ; BF ; CE ct nhau ti H.a)Chng minh t gic BECF ni tip ng trn . Xc nh tm I ca ng trn b)Chng minh DB.DC = DH.DA c)Chng minh ng thng k t A v vung gc vi EF i qua 1 im c nh d)Gi M v N ln lt l trung im ca BE v CF. Chng minh M , D , I , N cng thuc mt ng trne)Nu IA l phn gic ca gcEIF . Tnh s o gc BCE 13www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 15

THAM KHO THI TUYN SINH VO LP 10 Bai 1Giai cac phng trnh va he phng trnh : a. x4 3x2 54 = 0 b. 5x 4 1 x 6 = 0c.x2 3|x| 28 = 0d.5 3 8 52 3 5 =+ = x yx ye. 2 3 53 2 4 2 = =x yx yf.253 15 + = =x yx y Bai 2 Rut gon cac bieu thc :a. A =6 26 15 3 26 15 3| | |\ .+ + b. B =( 3 4) 19 8 3 3 + +c. C =1 1 1 2:1 2 1| || | | ||\ . \ .+ + x xx x x x d. D= 7 1 2 2 2:4 42 2 2| | | | || ||\ . \ . + + + +a a a a aa aa a av tm gi tra D = 1 Bai 3Cho (P) : y = 24xva (d): y = x + mtren cung mp Oxy a. Khi m = 1 , hay ve (P) va (d) .Tm toa o giao iem cua (P) va(d) bang pheptoanb. Tm m e (P va (d) tiep xuc nhau. Tm toa o tiep iemc. Xac nh gia tr m e (P) va (d) cat nhau tai hai iem A va B sao cho 2 232 + =A Bx xBai 4Cho phng trnh : x2 5x + m 2 = 0a. Tm ieu kien cua m e phng trnh co hai nghiem x1 ; x2

b. Tm gia tr m biu thc A = 2 2 21 2 2( 1) x x x t gi tr nh nhtc. Tm m e phng trnh co hai nghiem thoa : 3x1 8x2 = 26Bai 5ChoAABC co ba goc nhon noi tiep ng tron (O;R) va AB < AC. Ba ng cao AD , BE , CF cat nhau tai H. Goi I la trung ie m BC a. Chng minh cac t giac BFEC va DHEC noi tiepb. Ve ng knh AK cua (O). Chng minh BH = KC va H , I , K thang hangc. KH cat (O) tai N, EF cat BC tai M . Ch ng minh NFHE noi tiepd. Chng minh ba im A , N , M thang hange. Goi Q va G lan lt la trung iem BF va EC. Chng minh QDG ~AFHE f. So sanh dien tchAAHI va dien tchAAOI 14www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 16 THI TUYN SINH LP 10 TP HCM NM HC 2006-2007 Thi gian lm bi: 120 pht (khng k thi gian giao ) Bi 1 Gii cc phng trnh v h phng trnh sau : a)3x 2y 15x 3y 4+ =+ = b) 2x2 + 2 3 x 3 = 0c) 9x4 + 8x2 1 = 0 Bi 2Rt gn cc biu thc sau : a)15 12 1A2 3 5 2=

b)B =a 2 a 2 4aa 2 a 2 a| || | | | |\ .\ . + + ( a > 0; a=4 ) Bi 3Cho manh at hnh ch nhat co dien tch 360 m2. Neu tang chieu rong 2m va giam chieu dai 6m th dien tch manh at khong oi. Tnh chu vi cua manh at luc ban au Bi 4a) Viet phng trnh ng thang (d) song song vi ng thang y = 3x + 1 va cat truc tung tai iem co tung o bang 4.b) Ve o th cua cac ham so y = 3x + 4 va y = 2x2 tren cung mot he truc toa o. Tm toa o cac giao iem cua hai o th ay bang phep tnh. Bi 5Cho tam giac ABC co ba goc nhon va AB < AC. ng tron tam O ng knh BC cat cac canh AB, AC theo th t tai E va D.a) Chng minh AD.AC=AE.AB.b) Go i H la giao iem cua BD va CE, goi K la giao iem cua AH va BC.Chng minh AH vuong goc vi BC.c) T A ke cac tiep tuyen AM, AN en ng tron (O) vi M, N la cac tiep iem. Chng minh ANM AKM =d) Chng minh ba iem M, H, N thang hang. www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 17 THI TUYN SINH LP 10 TP HCM NM HC 2007-2008 Thi gian lm bi: 120 pht (khng k thi gian giao ) Cu 1: (1,5 im)Gii cc phng trnh v h phng trnh sau: a) x2 2 7 x + 3 = 0 b) x4 13x2 + 36 = 0c) 3 5 27 2 32+ = =x yx y Cu 2: (1,5 im)Thu gn cc biu thc sau: a) 7 4 36 2 2=A b) (3 2 10) 7 3 5 = + BCu 3: (1 im) Mt khu vn hnh ch nht c din tch bng 621 m2 v c chu vi bng 100 m. Tm chiu di v chiu rng ca khu vn. Cu 4: (2 im) Cho phng trnh x2 2mx + m2 m + 2 = 0 vi m l tham s v x l n s. a) Gii phng trnh vi m = 2. b) Tm m phng trnh c hai nghim phn bitx1 , x2. c) Tm m phng trnh c hai nghim ta mn : x1 x2 - x1 - x2 = 0 d)Tm iu kin m biu thc A = x12 + x22 t gi tr nh nht Cu 5: (4 im) Cho tam gic ABC c ba gc nhn (AB < AC). ng trn ng knh BC ct AB, AC theo th t ti E v F. Bit BF ct CE ti H v AH ct BC ti D. a) Chng minh t gic BEFC ni tip v AH vung gc vi BC. b) Chng minh AE.AB = AF.AC. c) Gi O l tm ng trn ngoi tip tam gic ABC v K l trungim ca BC. Tnh t sOKBCkhi t gic BHOC ni tip. d) Cho HF = 3 cm, HB = 4 cm, CE = 8 cm v HC > HE. Tnh HC. www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 18 THI TUYN SINH LP 10TP HCM NM HC 2008-2009 Thi gian lm bi: 120 pht (khng k thi gian giao ) Cu 1 Gii cc phng trnh v h phng trnh sau: a) 2x2 + 3x 5 = 0 b) x4 3x2 4 = 0c) 2x y 13x 4y 1+ =+ = Cu 2a) V th (P) ca hm s y = x2 v ng thng (D): y = x 2 trncng mt cng mt h trc to . b) Tm to cc giao im ca (P) v (D) cu trn bng php tnh. Cu 3Thu gn cc biu thc sau: a) A =7 4 3 7 4 3 +b) B = x 1 x 1 x x 2x 4 x 8.x 4x 4 x 4 x| | | |\ .+ + + + (x > 0; x 4). Cu 4 Cho phng trnh x2 2mx 1 = 0 (m l tham s) a) Chng minh phng trnh trn lun c 2 nghim phn bit. b) Gi x1, x2 l 2 nghim ca phng trnh .Tm m 2 21 2 1 2x x x x 7 + = . Cu 5 T im M ngoi ng trn (O) v ct tuyn MCD khng i qua tm O v hai tip tuyn MA, MB n ng trn (O), y A, B l cc tip im v C nm gia M, D. a) Chng minh MA2 = MC.MD. b) Gi I l trung im ca CD. Chng minh rng 5 im M, A, O, I , B cng nm trn mt ng trn. c) Gi H l giao im ca AB v MO. Chng minh t gic CHOD ni tip c ngtrn. Suy ra AB l phn gic ca gc CHD. d) Gi K l giao im ca cc tip tuyn ti C v D ca ng trn (O).Chng minh A, B, K thng hng. www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 19 THI TUYN SINH LP 10TP HCM NM HC 2009- 2010 Thi gian lm bi: 120 pht (khng k thi gian giao ) Cu 1 Gii cc phng trnh v h phng trnh sau: a) 8x2 2 x 1 = 0b) x4 2x2 3 = 0 c) 2x 3y 35x 6y 12+ = = d) 23 2 6 2 0 x x + = Cu 2a) V th (P) ca hm s y = 22x v ng thng (D): y = x + 4 trncngmt h trc to . b) Tm to cc giao im ca (P) v (D) cu trn bng php tnh. Cu 3Thu gn cc biu thc sau: a)A = 4 8 153 5 1 5 5 ++ + b) B = y y:1 xy1 xy 1x x x xyxy| | | | +\ .+ + Cu 4 Cho phng trnh x2 (5m 1)x + 6m2 2m = 0 (m l tham s) a) Chng minh phng trnh trn lun c 2 nghim phn bit vi mi m b) Gi x1, x2 l 2 nghim ca phng trnh .Tm m 2 21 2x x 1 + = . Cu 5Cho tam gic ABC (AB < AC) c ba gc nhn ni tip ng trn (O ; R). Gi H l giao im ca ba ng cao AD , BE , CF . Gi S l din tch ca tam gic ABC. a)Chng minh cc t gic AEHF v AEDB ni tipb)V ng knh AK ca ng trn (O). Chng minhAABD vAAKC ng dng Suy ra AB.AC = 2R.AD vS = . .4AB AC BCR c)Gi M l trung im BC. Chng minh t gic EFDM ni tipd)Chng minh OC vung gc vi DEv (DE + EF + FD).R = 2S www.VNMATH.com www.VNMATH.comTi liu thi vo lp 10 Gv : Lu vn Chung 20 THI TUYN SINH LP 10TP HCM NM HC 2010- 2011 Thi gian lm bi: 120 pht (khng k thi gian giao ) Bi 1: (2 im) Gii cc phng trnh v h phng trnh sau : a) 22 3 2 0 x x =c) 4 24 13 3 0 x x + =b) 4 16 2 9x yx y+ = =d) 22 2 2 1 0 x x = Bi 2: (1,5 im) a) V th (P) ca hm s 22xy = v ng thng (D): 112y x = trn cng mt h trc to . b) Tm to cc giao im ca (P) v (D) bng php tnh. Bi 3: (1,5 im) Thu gn cc biu thc sau: 12 6 3 21 12 3 A = + 2 25 35 2 3 3 5 2 3 3 52 2B| | | |= + + + + + || ||\ . \ . Bi 4: (1,5 im)Cho phng trnh 2 2(3 1) 2 1 0 x m x m m + + + =(x l n s) a) Chng minh rng phng trnh lun lun c 2 nghim phn bit vi mi gi tr ca m. b) Gi x1, x2 l cc nghim ca phng trnh. Tm m biu thc sau t gi tr ln nht: A = 2 21 2 1 23 x x x x + . Bi 5: (3,5 im) Cho ng trn tm O ng knh AB=2R. Gi M l mt im bt k thuc ng trn (O) khc A v B. Cc tip tuyn ca (O) ti A v M ct nhau ti E. V MP vung gc vi AB (P thuc AB), v MQ vung gc vi AE (Q thuc AE). a)Chng minh rng AEMO l t gic ni tip ng trn v APMQ l hnh ch nht. b)Gi I l trung im ca PQ. Chng minh O, I, E thng hng. c)Gi K l giao im ca EB v MP. Chng minh hai tam gic EAO v MPB ng dng. Suy ra K l trung im ca MP. d)t AP = x. Tnh MP theo R v x. Tm v tr ca M trn (O) hnh ch nht APMQ c din tch ln nht . www.VNMATH.com www.VNMATH.com