MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
5 than hi ^4X Y =
^4X - Y = 1 14X = 7 1 I b) Dat - = X ; — ^ X y - 2 1!),/
= Ỵ He phiTdng trinh trd thanh
Ta CO : < 2X + 3Y = 4 4X - Y = 1 2X + 3Y = 4 12X-3Y = 3 2X + 3Y = 4 x = l 2 2.12 + 3Y = 4 X = -2 o 3Y = 3 X = -2. Y = 1
Cty TNHH MTV DWH KhanQ Vift
Do do 1 = 1 X " 2
1 = 2
y - 2 = 1 1" = = 2
[ y - 2 = l [y = 3
Vay he phifdng trinh da cho c6 nghiem la (x ; y) = (2 ; 3)
Bai 3: Doi : 30 phut = - g i d
Gpi van toe ban dau cua ngi/tJi di xe dap la x (km/h) (Dieu kien x > 0)
Thtti gian dif dinh di tir A den B la : 50 : x = — (h)
X Quang dúcfng di diTdc sau 2 gid la : x.2 = 2x (km) Quang dúcfng di diTdc sau 2 gid la : x.2 = 2x (km) Quang dÚdng eon lai lii : 50 - 2x (km)
Van toe di tren quang difdng con lai la : x + 2 (km/h)
Thdi gian di Ircn quang dúdng con lai la : (50 - 2x) : (x + 2) = ——^ (h)
X H~ ^ , , 5 0 - 2 x 1 - 50 ^.^ , ,f , , 5 0 - 2 x 1 - 50 ^.^ , ,f Theo dau hai ta c6 phifdng tnnh : + - + 2 = — (*) ' X + 2 2 X (*)c^ 2x(50 - 2x) + 5x(x + 2) = 50.2(x + 2)
o lOOx - 4x' + 5x' + lOx = lOOx + 200 o x' + lOx - 200 = 0
Á= 25 + 200 = 225, VÁ = 15
X, = ll±ll = 10 (thieh hdp); X2 = ^^Y^ = -20 (khong thich hdp, vi -20 < 0)
Vay van tóc ban dau cua ngUtJi di xe dap la 10 km/h. '»
Nhan xet : Giai bai toan bing each lap phiTdng trinh loai toan chuyen dong,
dang loan nay cung quen ihuoc doi vdi mpi hoc sinh Idp 9. pi;
Bai 4: a) Tỉ giac BHCD la hinh binh hanh (gt) ^ =>BH//DC, CH//DB. Ma B H l A C . C H l AB
(H la irifc tarn cua tarn giac ABC) / H G\ Nen AC 1 DC, AB 1 DB
=0 ACD = 90", ABb = 90".
_ N D
(H la trifc tarn cua tam giac ABC) va DE // BC (gt) => DE 1 AH =^ AED = 90"
Luygn gi^i trirdc ki thi vio I6p 10 ba mjgn BJc, Trung. Nam mOn Toan _ Nguygn Dijfc TSn
k i n h A D . V a y A, B, C, D, E c u n g t h u p c m o t d i T d n g t r o n .
b) X6t dtfdng tron (ABCDE) c6 DE // BC => DE = BC => BAE = DAC
c) O la tam difdng tron ngoai tiep tam giac ABC (gt) => O la trung diem cua doan thing AD.
TiJ giac BHCD la hinh binh hanh (gt), M la trung diem canh BC (gt) ' => M la trung diem cua doan thang HD. ^ ;, Xet AAHD c6 AM va HO la hai dúdng trung tuyen cát nhau tai G
2
=> G la trong lam cua lam giac AHD => AG = — AM.
Xet AABC CO AM la dúdng trung tuyen, G nhm tren doan thang AM va
AG = ^ AM. Vay G la trpng tam cua tam giac ABC. d) Goi N la diem doi xi^ng cua O qua M.
Tur giac BOCN c6 M la trung diem ciia ON va BC => TO giac BOCN la hinh binh hanh.
Ma OB = OC (= a) ncn BOCN la hinh Ihoi =^ NB = NC = OB = OC - ạ Mat khac, la co OM = ^ AH (OM la dudng trung binh cija tam giac AHD) va OM = ^ ON. Suy ra AH = ON. Ma AH // ON (cung vuong goc vdi BC). Do do AONH la hinh binh hanh => NH = OA = ạ
Ta CO : NB = NH = NC = ạ
=> DiTcJng Iron ngoai tiep tam giac BHC c6 tam la N, ban kinh la ạ
Do vay do dai diTdng iron nay la 2na (dvđ)
Nhan xet : Day cung la bai loan quen thuoc, liTu y rkng ncu hai tam giac c6
chung dirdng trung tuyen thi chung c6 chung trong tam. , ••.,.>' // r \]6s624
DE THI TUYÍN SINH LdP 10 THPT, TJNH BINH D!NH NAM HOC 2011 - 2012
Bai 1: (2 diem)
fix - y = 7 a) Giai he phúdng Irinh : \[2x + y = 8
b) Cho hhm so y = ax + b. Tim a vạ b biet r^ng do thj cua ham so" da cho song
song vdi duTcfng thing y = -2x + 3 va di qua diem M(2; 5).
Cty TNHH MTV DWH Khang Vj^t
pai 2: (2 diem) Cho phiTdng trinh x^ + 2(m + l)x + m - 4 = 0 (vdi m la tham s6')
ji) Giai phúdng trinh da cho khi m = - 5 . -; i '
b) ChiJng to phúdng trinh da cho luon cd hai nghiem phan biet vdi mpi gid irj cua tham sóm.
c) Tim m de phúdng trinh da cho cd nghiem Xi, X2 thda man he thtfc: , xf + X2 + 3X|X2 = 0 xf + X2 + 3X|X2 = 0
Bai 3: (2 diem) Mot manh dát hinh chỉ nhat cd chieu dai hdn chieu rpng 6m va binh phúdng cua so do dp dai dúdng cheo gap 5 Ian so do cua chu vị Tinh dien tich cua manh dát hinh chỉ nhat da chọ
Bai 4: (3 diem) Cho dúdng iron tam O vk BC la day cung khong di qua lam.
Tren tia doi cua tia BC lay diem M sao cho M khong trung vdi B. Dudng lhang di qua M cit dúdng iron (O) da cho tai N va P (N nam gitfa M va P) sao cho O n^m ben trong PMC. Gpi A la diem chinh giiía cua cung nho NP. Cdc day AB va AC Ian lifdl cat NP tai D va Ẹ
a) Chtfug minh liJ giac BDEC npi tiep. b) Chu-ng to MB.MC = MN.MP
c) OA cat NP tai K. ChiJng minh MK^ > MB.MC
Bai 5: (1 diem) Tim gia Iri nho nhat ciia bieu thijfc A = Hl/CfNG DAN GIAI x^ - 2 X + 2 0 1 1 (vdi X ^ 0) Bail: a) Ta cd : 3x - y - 7 [2x + y = 8 <=> i 5x = 15 2x + y = 8 X =y = 2" 3
Vay he phúdng trinh da cho cd nghiem duy nhat (x ; y) = (3 ; 2) b) Gpi (d) va (d') Ian liTdt la do thi cua ham so y = ax + b va y = -2x + 3.
a = - 2
(d) // (d') o b ^ 3 '. Vdi a = -2, ham so da cho \rd thanh y = -2x + b (d)
(d) di qua M(2 ; 5) o yw = - 2 . X M + b O 5 = -2.2 + b o b = 9 Vay a = - 2 va b = 9.
Nhan xet: Day la bai loan quen thupc dói vdi mpi hpc sinh Idp 9. ^ai 2: a) Khi m = - 5 . phiTdng trinh da cho trd thanh:
- 8x - 9 = 0 (vdi a = 1 ; b = - 8 ; c = -9) (*)
(*) CO cac he so thoa man a - b + c = 0 nen nghiem cua phiTdng trinh (*) 1^ :
Luy$n giai tru6c kl thi vAo lOp 10 ba mien B.iL. i iịiiỵ Nam mOn Toan _ NguySn Pijfc Tin
Vay khi m = -5, phirdng trinh da cho c6 hai nghiem phan biet Xi = - 1 va X2 = 9. b) Á = (m + 1)^ - (m - 4) = m + 2m + 1 - m + 4 = m + m + 5 \2 ( 1 m + — V 2) 19 ^ . + — > 0, vdi moi m. 4 .m a/
Vay phi/dng trinh da cho luon c6 hai nghiem phan biSt vdi moi m.
X, + x j = -2(m + 1 ) c) Theo he thuTc Vi-et, ta c6 •
X|X2 = m - 4 Do d6 \] + x\ 3x|X2 = 0 <=> (X| + X2)^ + X1X2 = 0 o [-2(m + l ) f + ( m - 4 ) = 0<=>4m^ + 8m + 4 + m - 4 = 0 i5' i o 4m^ + 9m = 0 m(4m + 9) = 0 o -9 m = 0 4m + 9 - 0 <=> m = 0 9- m = — 4
Vay m = 0 hoSc m = — thi phifdng trinh da cho c6 hai nghiem Xi, X2 thoa he thijrc: 4
xf + X2 + 3x,X2 = 0
Nhan xet: Day la bai toan de ve van dung he thufc Vi-et.
Bai 3: Goi do dai cua chieu rong manh dat hinh chff nhat da cho la x(m) (Dieu kien x > 0)
Chieu dai cua manh dat hinh chỉ nhat da cho la x + 6 (m)
Chu vi cua manh dat hinh chff nhat nay la : 2(x + x + 6) = 4x + 12 (m)
Theo dinh li Py-ta-go ta c6 binh phiTdng do dai cua dirdng cheo hinh chu" nhai la x^ + (x + 6 ) l ' f.r:cr.,-;frr:.>l5:'&
Theo dau bai, ta c6 phi/dng trinh :
x S (X + 6)^ = 5(4x + 12) x^ + x^ -I- 12x -1- 36 = 20x -I- 60 o x^ - 4x - 12 = 0 Á = 4 + 12= 16, VA' = 4 ^X, = ^ ^ = 6 ( n h a n ) ; X 2 = ^ - ^ = -2(loai) Vay|;hieu rong cua manh dat da cho la 6m, chieu dai cua manh dat da cho la: ' -6 = 12 (m)
Dỉn uch manh dat da cho la : 6.12 = 72 (m^)
Nhan xet : Giai bai toan bing each lap phiTdng trinh c6 npi dung hinh hoc. day la dang toan rat quen thupc vdi hoc sinh Idp 9.
Bai 4:
a) Ta CO : AED = ^ ^ ^ ^ + sdPC ^^^^ ^^^^ ^ ^^^^^ ^^^^^ ^^^^ ^^^^
Cty TNHij Miv DVVH Khang Vijt
ABC = sdAC sdAP + sdPC
Ma AN = AP (gt). Do d6 AED = ABC => Tu" giac BDEC npi tiep.