THI KIEM TRA CHAT LNG HOC KY II

THI KIEM TRA CHAT LNG HOC KY II . Nam hoc 2009 - 2010 MON : TOAN 8 - THI GIAN : 90 phut

Trng THCS Tan Hi Lp :

Ho va Ten : Li phe cua GV iem

E 1 . I/ LY THUYET : ( 2 )

Cau 1/ Neu nh ngha phng trnh bac nhat mot an ? Cho v du . ( 1) Cau 2/ Neu nh ly thuan cua Ta Let ? ( 0,5 ) * Ap dung : Cho hnh ve ( 0,5 )

Biet BC song song vi MN ; AB=25cm ;

BM=15cm ; AC=30cm . Tm x = ?

II/ BAI TAP : ( 8 )

Bai 1/ Giai cac phng trnh sau:

a/ x 5 = -8 (1) b/

EMBED Equation.3 ( 0,5 ) Bai 2/ Giai bat phng trnh va bieu dien tap nghiem tren truc so .

6x + 12 4x 8 (1) Bai 3/ Hai xe o to khi hanh cung mot luc t hai a iem Ava B cach nhau 80km , va sau mot gi th hai xe gap nhau . Tnh van toc cua moi xe ? Biet xe i t A co van toc ln hn xe i t B la 10km / h . (1,5) Bai 4 / Cho tam giac ABC vuong goc tai A vi AB = 6cm , AC = 8cm . Ve ng cao AH

a/ Chng minh : ABC ong dang HAC . Suy ra : AC2 = HC . BC (1,5) b/ Tnh o dai BC va AH (1) c/ Ke CM la phan giac cua goc ACB ( M thuoc AB ) . Tnh o dai CM ? (1,5) AP AN E I :

A. LY THUYET : Cau 1/ Tra li va cho v du ung 1 Cau 2/ Tra li ung 0,5 va tnh x = 18 0,5

B . BAI TAP : Bai 1/ x 5 = - 8 x = -8 + 5 0,5

x = - 3 . Vay PT co tap nghiem S= 0,5 b/

EMBED Equation.3

EMBED Equation.3 * TH1/

x 3 + 2x = 9 khi x 3 0 x 3

3x = 12 x = 4 ( TM ) 0,25 * TH2 /

- x + 3 + 2x = 9 khi x 3 0 x 3 x = 6 ( ko TM ) 0,25

Vay PT a cho co tap nghiem S=

Bai 2 / 6x + 12 4x 8 6x 4x - 8 12 2x - 20 x - 10 0,5

Bieu dien ung 0,5

Bai 3 / Goi van toc xe i t B la x ( km/h ) . x 0

Van toc xe i t A la : x + 10 ( km/h)

Do sau mot gi hai xe gap nhau nen ta co phng trnh :

x + ( x + 10 ) = 80 1

2x = 70 x = 35 (TM )

Vay van toc xe i t B la 35km/h va van toc xe i t A la 45 km/ h 0,5 Bai 4 / ve hnh ung 0,5

a/ Xet hai tam giac vuong ABC va HAC co : goc ACB chung

nen ABC ong dang HAC

Suy ra : AC2 = BC . HC . 1 b/ Theo Py Ta Go ta co : BC = = 10 0,5

T cau a/ suy ra : HA = = 4 ,8 0,5

c/ Do CM la phan giac cua goc ACB nen ta co :

va ap dung tnh chat cua day t so bang nhau 1 Suy ra : MA =

EMBED Equation.3 . Theo PyTaGo : MC = 0,5 E 2 . I/ LY THUYET : ( 2 )

Cau 1/ Neu hai quy tac bien oi phng trnh ? ( 0,5 ) Ap dung : Giai phng trnh : 3,2x = - 16 ( 0,5 ) Cau 2/ Neu tnh chat ng phan giac cua tam giac ? (0,5) Ap dung : Cho tam giac ABC , phan giac trong cua goc A cat BC tai M . Biet AB = 8cm , AC = 10cm, MB = 4cm . Tnh o dai MC =? (0,5) II / BAI TAP : ( 8)

Bai 1/ Giai cac phng trnh sau :

a/ x + 8 = 3 (1) b/ (0,5) Bai 2/ Giai bat phng trnh va bieu dien tap hp nghiem tren truc so

7x 12 3x + 4 (1) Bai 3/ Hai ngi i xe ap cung mot luc , ngc chieu nhau t hai a iem Ava B cach nhau 44km va gap nhau sau hai gi . Tnh van toc cua moi ngi . Biet rang van toc cua ngi i t A i nhanh hn van toc ngi i t B la 4km /h . (1,5)Bai 4/ Cho tam giac ABC vuong tai A co AB = 8cm , AC = 15cm , AK la ng cao .

a/ Chng minh : ABC ong dang KBA (1,5) b/ Tnh o dai BC va AK . (1) c/ T K ke KM AB ( M thuoc AB ) ; KN AC ( N thuoc AC ) Chng minh : AM . AB = AN . AC (1,5)AP AN E II A. LY THUYET : Cau 1/ Tra li ung hai quy tac 0,5

Ap dung : x = - 5 0,5

Cau 2/ Neu ung tnh chat tia phan giac cua tam giac 0,5

Ap dung : Tnh ung MC = 5 cm 0,5

B . BAI TAP :

Bai 1/ a/ x + 8 = 3 x = 3 8 0,5

x = - 5 0,5

b/

EMBED Equation.3 * TH1 : x 5 +2x = 7 khi x 5 0 x 5

3x = 12 x = 4 ( ko TM ) o,25

* TH 2 : - x + 5 + 2x = 7 khi x 5 0 x 5

x = 2 ( TM ) 0,25 Vay phng trng co tap nghiem S =

Bai 2/ 7x 12 3x + 4 7x 3x 4 + 12 0, 25 4x 16 x 4 0 ,25

bieu dien ung 0.5

Bai 3 / Goi van toc xe i t B la x ( km/h ) , x 0

Van toc cua xe i t A la : x + 4 ( km/h )

Do sau hai gi hai xe gap nhau nen ta co phng trnh :

2x + 2 ( x + 4 ) = 44

4x = 36 x = 9 ( TM )

Vay van toc cua xe i t B la 9 km/h va van toc cua xe i t A la 13 km/h Bai 4/ Ve hnh ung 0,5 a/ Hai tam giac vuong ABC va KBA co goc ABC chung nen Tam giac ABC ong dang tam giac KBA 1 b/ Theo Py Ta Go ta co : BC = = 17 0,5 Do tam giac ABC ong dang tam giac KBA nen

Suy ra : KA = = = 0,5 c/ Chng minh hai tam giac KAB va MAK . Nen suy ra AK2 = MA . AB (1) 0,75

Tng t chng minh hai tam giac KAC va NAK . Nen AK2 = NA . AC (2) o,75T (1) va (2) Suy ra : MA . AB = NA . AC

E 3 I/ LY THUYET : ( 2 )

Cau 1/ Neu cac bc giai phng trnh cha an mau ? ( 0,5 ) Ap dung : Giai phung trnh ( 0,5 ) Cau 2/ Neu he qua cua nh ly Ta -Let trong tam giac ? ( 0,5 ) Ap dung : Cho hnh ve , hay tm x ( 0,5 )

Biet HK song song vi QR II/ BAI TAP : Bai 1/ Giai cac phng trnh sau : a/ x + 12 = 5 (1) b/ (0,5) Bai 2/ Giai bat phng trnh va bieu dien tap hp nghiem tren truc so

2 4x 6 3x (1) Bai 3/ Mot o to chay tren quang ng AB . Luc i o to chay vi van toc 30km/h , luc ve o to chay vi van toc 40km/h . V vay thi gian ve t hn thi gian i la 20phut . Tnh quang ng AB ? (1,5) Bai 4/ Cho tam giac ABC vuong tai A co AB = 9cm, BC = 15cm . AH la ng cao

a/ Chng minh : ABC ong dang HAC (1,5) b/ Tnh o dai AC va AH . (1) c/ Goi M la trung iem cua BC . Ke MI vuong goc vi AC ( I thuoc AC ).

Tnh t so dien tch cua CMI va CBA . Suy ra dien tch tam giac CMI (1,5)AP AN E III A/ LY THUYET : Cau 1 / Neu ung cac bc giai phng trnh cha an mau 0,5

Ap dung : KX : x 3 ; 3x 6x + 18 = 0 x = 6 0,5 Cau 2/ Neu ung he qua cua Ta Let 0,5

Ap dung : Tnh ung x = 7,5 0,5

B/ BAI TAP : Bai 1/ a. x + 12 = 5 x = 5 12 0,5 x = -7 0,5

b/ * TH1 : x 3 + 3x = 9 khi x 3 0 x 3

4x = 12 x = 3 ( TM ) TH2 : - x + 3 + 3x = 9 khi x 3 0 x 3

2x = 6 x = 3 ( khong TM ) Vay PT co tap nghiem S =

Bai 2/ 2 4x 6 3x -4x + 3x 6 2 0,25 x -4 0,25

Bieu dien ung 0,5

Bai 3 / Goi quang ong AB la x (km ) , x 0 20 phut = 2/3 h 0,25 Thi gian luc i la h 0,25 Thi gian luc ve la : h 0,25 Theo bai rata co phng trnh : - = 0,25 Giai ra ta co : x = 80 (TM) . Vay quang ng AB dai 80 km 0,5 Bai 4/ Ve hnh ung 0,5 a./ Hai tam giac vuong ABC va HAC co goc ACB chung nen

Tam giac ABC ong dang tam giac HAC b/ Theo Py Ta Go Ta co : AC = = 12 cm

Do hai tam giac ABC va HAC ong dang . Nen

Suy ra AH = = = 7,2 cm c/ Chng minh hai tam giac vuong CMI va CBA ong dang . Suy ra =

Nen S= = = cm2 E 4 I/ LY THUYET : ( 2 )

Cau 1/ Neu hai quy tac bien oi bat phng trnh ? ( 0,5 ) **Ap dung : x 7 12 ( 0,5 )

Cau 2/ / Neu he qua cua nh ly Ta Let trong tam giac ? ( 0,5 ) ** Ap dung : Cho hnh ve , hay tm x ( 0,5 ) Biet MN song song vi BC

II / BAI TAP : ( 8 ) Bai 1/ Giai cac phng trnh sau :

a/ x + 7 = 13 (1) b/ ( 0,5 ) Bai 2/ Giai bat phng trnh va bieu dien tap hp nghiem tren truc so

7x 10 5x + 4 (1) Bai 3/ Mot ngi i xe ap t A en B vi van toc 12km/h . Luc ve ngi o ch i vi van toc la 10 km/h nen thi gian ve nhieu hn thi gian i la 45 phut . Tnh quang ng AB ? (1,5) Bai 4/ Cho tam giac ABC vuong tai A co AH la ng cao . Biet AB = 15 cm , AH = 12cm

a/ Chng minh : ABC ong dang HBA ( 1,5 )

b/ Tnh BH , AC , HC (1) c/ Tren AC lay iem E sao cho CE = 5cm , tren BC lay iem F sao cho CF =4cm Chng minh tam giac CEF vuong . Suy ra : CE . CA = CF . CB (1,5)AP AN : E 4

A. LY THUYET : Cau 1/ Neu ung hai quy tac bien oi bat phng trnh 0.5 Ap dung : x 7 12 x 12 + 7 x 19 0,5 Cau 2/ Neu ung he qua cua Ta Let cua tam giac 0,5

Ap dung : Tnh ung x = 7,5 cm 0,5

B . BAI TAP : Bai 1/ a . x + 7 = 13 x = 13 7 0,5

x = 6 0,5

b/ * TH1 : x 6 + 2x = 9 khi x 6 0 x 6 3x = 15 x = 5 ( Ko TM ) TH2 : -x + 6 + 2x = 9 khi x 6 0 x 6

x = 3 (TM ) . Vay PT co tap nghiem S =

Bai 2/ 7x 10 5x + 4 7x 5x 4 + 10 2x 14 x 7 0,5 ** Bieu dien ung 0,5

Bai 3 / Goi quang ng AB la x (km ) x 0 . 45phut = h Thi gian luc i la (h) Thi gian luc ve la (h) Theo bai ra ta co - = Giai ra ta co : x = 45 (TM ) . Vay quang ng AB dai 45km Bai 4/ Ve hnh ung 0,5 a/ Hai tam giac vuong ABC va HBA ong dang v co goc ABC chung 0,5

b/ Theo py ta go ta co : BH = 9cm ; Do hai tam giac ABC va HBA ong dang suy ra AC = 20

Tnh BC = 25 cm ; suy ra HC = BC HB = 25 9 = 16 cm c/ Ta co : ; . Nen , Suy ra EF song song AH Ma AH BC nen EF BC . Hay tam giac CEF vuong tai F . Chng minh hai tam giac CEF va CBA ong dang . Suy ra : CE . CA = CF . CB _1301320436.unknown

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