M, D, E ,N thang hang ^ J,
d) Tac6: SABI C= SAB C+ Siec
I K / / B C (cmt) => SiBc = SKBC (VI C6 ciJng chieu cao va canh d^y B C )
1
= > SABIC - SABC + SKBC = SABKC = — B C . A K
Ta lai c6: A C B - A B C = (90" - C A K ) - (90" - B A K ) = B A K - C A K B I K C la hinh thang can ^ B I = C K = > B I = C K (lien he giffa cung v^ day) => B A I = C A K (2 g6c npi tiep ch^n 2 cung b^ng nhau)
" _ - - I A K = 30"
=> ACB - ABC = B A K - B A I = l A K :
Xet AAIK vuong tai K c6: A K = AIcos l A K = 2Rcos30" = R 73 a (<;
£ . -Vay: SAB.C = ^ B C . A K = i . ^ ^ .RS = R ' ^ Vay: SAB.C = ^ B C . A K = i . ^ ^ .RS = R ' ^
LuyQn qiai ai troflc kl thi vAo I6p 10 ba m\6n B&c, Trung, Nam mfln T , i ::juySn Ddc JSn
D6 SO 75
Bai 1: (3 diem)
a) Ve do thi cua ham s6' y = 2x - 4.
fx = 2 y- 3 ^ M-'^
b) Giai he phiTcfng trinh: <^ . [y = 2x - 3
c) Rut gon biéu thtfc: P = - + ^ vdi a > 0.
a^+2a
Bai 2: (2 diem) Cho phiTdng trinh: x^ - 3x + m = 0 (1) (x la an) a) Giai phUdng trinh (1) khi m = 1.
b) Tim cac gia tri m de phiTrtng trinh (1) c6 hai nghiem phan biet X|, X2 thoa man:
7x? + 1 + ^x^ + 1 = 3 N/3
Bai 3: (1 diem) Khoang cdch giffa hai ben song A va B la 48 km. Mot ca no di
tii hen A den ben B, roi quay lai ben Ạ Thdi gian ca di va ve la 5 gift
(khong tinh thdi gian nghi). Tinh van toe cua ca no trong nifdc yen iSng, biet r^ng van toe cua dong niTdc la 4 km/h.
Bai 4: (3 diem) Cho hinh vuong ABCD c6 do dai canh b^ng a, M la diem thay
đi tren canh BC (M khdc B) va N la diem thay đi tren canh CD (N khdc C) sao cho MAN = 45". Du-dng cheo BD c^t AM va AN Ian liTdt tai P va Q. a) Chúng minh tiJ giac ABMQ la tỉ giac npi tiep.
b) Goi H la giao diem cua MQ va NP. Chúng minh AH vuong gdc vdi MN. c) Xac dinh vi tri diem M va diem N de tarn giac AMN c6 dien tich Idn nhat.
Bai 5: (1 diem) Chúng minh: â + b' > ab(a + b) vdi moi a, b > 0. Ap dung kcl
qua tren, chuTng minh bat ding thufc: 1 1
- r r + - : + — <1 a-^ + b^ + 1 b-^ + c^ + 1 c-^ + a-^ + 1
vdi moi a, b, c la cac so diTdng thoa man abc = 1.
Hl/dNG DAN GIAI
Bai 1: a) Do thi h^m so y = 2x - 4 c^t true Ox tai A(2; 0), c^t true tung Oy tai B(0;-4).
b) X = 2y - 3 fx = 3 y = 2 x - 3 ly = 3
:) • 9yla -yl25& + 44j = 9yfa-5y[a + 2a Va = 2 Văa + 2)
»~f 2a = ăa + 2)
Cty TNHH MTV D W H Khang Viet
Do do P = 2Va
Bai 2: a) m = 1 ta c6 phi/dng trinh: x ^ - 3 x + l = 0 , A = 9 - 4 = 5
3 + V5 3- V 5
• X , = • , X 2 =
b) (1) CO hai nghiem phan biet <=> A = 9 - 4 m > 0 <=> m < — (*)
4 Theo dinh li Vi-et: X| + Xi = 3 ; X|X2 = m. Binh phúdng ta dUdc:
X |+x?+2 + 2^'(xf + l)(x^ + l) = 27<:^ \; + \l + 2^K^\l + xf + x^ + 1 = 25
Tinh dMdc: xf + x, = (x, + X 2 ) ' - 2x|X2 = 9 - 2m va diTa he ihiJc tren vc dang:
Vm^ - 2m + 10 = in + 8 <i> ni^ - 2m + 10 = m' + 16m + 64 <=> 18m = -54
<=> m = -3. ThiY lai thay m = -3 thoa man phu"dng trinh va dieu kien (1).
Bai 3: Goi van toe ca no trong nifdc yen Idng Ui x (km/h, x > 4)
Van tóc ca-no khi núdc xuoi dong la x + 4 vli thdi gian ca-no chay khi núdc
48 xuoi dong la X -f 4
Van tdc ca-no khi nifdc ngiTrtc dong la x - 4 vii thdi gian ca-no chay khi núdc 48
ngúcfc dong la .
X - 4
• , . L 48 48 ^ '
Theo gia thiet ta co phiTdng trinh: -1- = 5
X + 4 X - 4 o 48(x - 4 + X + 4) = 5(x- - 16) o 5x^ - 96x - 80 = 0 o 48(x - 4 + X + 4) = 5(x- - 16) o 5x^ - 96x - 80 = 0
Giiii phúcfng trinh ta dÚde: x = -0,8 (loai), x = 20 (thoa man). ' ' Vay van tdc ca-no trong núdc yen lang la 20 km/h.
Bai 4: ' ' a) D A B / I M N Hinh2 Ve diTdc hinh 1. Theo gia thiet: QAM = 45" va QBM = 45"
QAM = QBM => Tú giac ABMQ la tỉ giac noi tiep b) ABMQ la tOr giac npi tiep suy ra AQM + ABM = I8O"
Luygn giai ae Iri^c kl ttii vao lOp 10 ba mien Bac, Trung, Nam mOn Toan _ Nguyfin Difc Tgn"
A B M = 90" => A Q M = 90" =ị M Q ± A N .
TiTdng tif ta c6 A D N P la 11? giac noi tiep => NP ± A M . j ;
^1, Suy ra H la tri/c tam cua tam giac A M N => A H J_ M N . la ui ! ;
C h u y : L a p luan trcn van dung khi M trung vdi C.