MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
a) Rut gon bieu thtfc P.
^) Vdi nhffng gia tri nao cua a thi P > ^ •
fiai 3: (2 diem) '
^) Tim toa do giao diem cua do thi cac ham so : y = x^ va y = - x + 2.
Luyen g\i\c ki thi v i o lap 10 ba miSn 6^0. Trung, Nam mOn ToAn _ NguySn Dufc Ta'n
X i , X2 thoa man dSng thufc : 5 - X 1 X 2 + 4 = 0.
Bai 4: (3 diem) Tren nijTa dUdng tron diTdng kinh AB, lay hai diem P, Q sao cho
P thupc cung AQ. Goi C la giao diem cua tia AP va tia BQ ; H la giao diem cua hai day cung AQ va BP.
a) Churng minh tiJ giac CPHQ npi tiep difdng tron. ^ , b) Chu-ng minh ACBP ^ AHAP.
c) Biet AB = 2R, tinh theo R gi^ tri ciia bieu thufc : S = AP.AC + BQ.BC.
25 ' •>
Bai 5: (1 diem) Cho cac so a, b, c deu \dn hdn — . Tim gia tri nho nhat cua
bieu thurc : Q = 2 V b- 5 2 ^ - 5 2 7^ - 5
Hl/dNG DAN GIAI
Bai 1: a) DiTdng thdng y = (2m - l)x + 3 song song vdi difdng thang y = 5x - 1
2 m - l = 5 3^-\ c:>2m = 6 o m = 3 b) 2x + y = 5 [4x + 2y = 10 [7x = 14 <=> < 3x - 2y = 4 X = 2 3.2-2y = 4 3x - 2y - 4 [3x - 2y = 4 X = 2 fx = 2 -2y = - 2 [y = 1
Vay nghiem cua he phiTdng trinh da cho la (x ; y) = (2 ; 1).
Nhgn xet : Day la cac bai toan rat quen thupc, cic em hoc sinh hay giai he
phiTdng trinh (cau b) b^ng phiTcfng phap thé.
Bai 2: «•* --'"' mYi\!h i i - v s n o , vnox fi +
1 1 a) P =
2^fa 1 + Va
f 1 l + ^fa-l + ^fa 1 + ^/a + 1
( 1 - V a ) ( l + 7 a ) ' Va ( i - V I ) ( i + V ^ ) ' v^ b) Vdi a > 0 va a ^ 1 thi: ^ 1 2 1 2 2 1- V ^ 2 1- V a _ i > 0 c . i z l ± £ > 0 o i ± ^ > 0 2 1 - Va 1 - Va o l - V a> 0< = > V a < l o 0 < a< l
Ta c6 0 < a < 1 ket hdp vdi dieu kien a > 0, a ^ 1 ta diTdc 0 < a < 1.
Nhan xet : Day cung 1^ c^c b^i todn quen thupc, tuy nhien mot so hoc sinh
Cty TNHH MTV DVVH Khang Vỉt
se m^c phai sai lam sau : 1 - Va > ^ c= > 4> l - Va<=>Vr>_3 <=>a>0.
3) phi/dng trinh hoanh dp giao diem cua do thi cac ham so y = x^ va y = -x + 2 la : x = - x + 2<=>x'' + x - 2 = 0 x = - x + 2<=>x'' + x - 2 = 0
Vi a + b + c = 1 + 1 + ( >-2) = 0 nen X , = 1, X2 = - =-2. a
, xi = 1 thiy, = - X | + 2 = - l + 2= l.Tpadpgiaodiemla Ăl ; 1).
• X2 = -2 thi y2 = - X 2 + 2 = 2 + 2 = 4. Tpa dp giao diem la B(-2 ; 4).
b) A = 1 - 4 + 4m = -3 + 4m. PhiTPng trinh c6 hai nghiem x,, X2 <=> A > 0 <:>-3 + 4m>0<=>4m>3c^m> - (*) <:>-3 + 4m>0<=>4m>3c^m> - (*)
4
Theo he thufc Vi-6t, ta c6 : X , + X 2 = 1 x, X 2 = 1 - m C Do d6 : 5 ^ 2 ; - X i X 2 + 4 = 0 o X | ; t 0 X , ;t 0 5( X 2 + X , ) - ( x, X 2 ) ^ + 4 X, X 2 = 0 <=> { o I m ^ 1 m ^ 1 m"" + 2m - 8 = 0 m = 2 m = -4" <=> { (m + 1)^ = 9 1-m 0 '^^ 5 - ( l - m ) ^ + 4 ( l - m ) = 0 m ^ 1 m + 1 = 3 hoSc m + 1 = -3
Ket hdp vdi dieu kien (*), ta c6 m = 2 la gia tri can tim.
Nhfin xet:
a) Bai tôn de, quen thupc. ' ' ' ' '
t^) Bai toan van dung he thiJc Vi-et, thiTdng mic phai sai lam, khong xet x, ^ 0, X2
0 va dieu kien de phúdng trinh c6 nghiem X), X2.
^ai 4: a) Ta c6 : APB = 90", AQB = 90"
(goc npi tiep ch^n nufa diTdng tron) =^ BP 1 AC, AQ 1BC
=> CPH = CQH = 90"
=^ Tỉ giac CPHQ npi tiep difdng tron.
Xet ACBP va AHAP c6 CPB = HPA (= 90"), CBP = HAP (hai g6c npi tiep ^^ng ch^n cung PQ cua diTdng tron (O)). Do do ACBP '^AHAP (g.g)
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Luy^n qiai 06 truflc kl thi vao I6p 10 ba mign B^c, Trung, Nam mOn Toan _ Nguygn Pijfc TSn