MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
caul 1) P xac dinh o
2) P = X - 1 ^ 0 - - '3 X + 1 ^ 0 o - 1 ;^ 0 3 6x - 4 x(x + 1) + 3(x - 1) - (6x - 4) X ^ 1 X ^ -1 X- 1 X + 1 X - 1 (X + l)(x - 1) x^ + X + 3x - 3 - 6x + 4 x^ - 2x + 1 (X -1)' x - 1 (x + l)(x-l) (x + l)(x-l) (x + l)(x-l) x + 1 Nhan xet: Day la bai todn ve phan thiJc dai so de va quen thupc.
'2x + y = -4
"_x-3y = 5
CSu 2. 1) a = 1. He phifdng trinh la
<=> < 6x + 3y = -12 [7x = -7
l x - 3 y = 5
X = -1 -1 - 3 y = 5 -1 - 3 y = 5
[ X - 3y = 5
• Vdi a = 1. He phúcfng trinh c6 nghiem (x; y) la (-1; 2)
2x + ay = -4 -5 + ax X = -1 y = -2 2) 2x + ay = -4 [2x + ay = -4 ax - 3y = 5 -3y = 5 + á^x y = -5 + ax 2x + ạ = -4 y = 3 -5 + ax 6x - 5 a + âx = -12 y = -5 + ax (â + 6) = -12 + 5a (1) y = -5 + ax
Vi â + 6 > 0, vdi moi a nen (1) c6 nghiem vdi moi ạ Do vay he phuTdng tni
CO nghiem (x; y) vdi moi ạ
Nhan xet: Day la bai todn ve he phúdng trinh bac nhat hai an, b^i todn ^ dói vdi moi hoc sinh Idp 9.
Cfiu 3. Goi chieu dai cua hinh chỉ nhat da cho la x(m) (Dieu kien x > 4) Chieu rong cua hinh chu* nhat la - (m)
Dien tich ciia hinh chff nhat da cho 1^: x. - = — (m^)
2 2
Cty TNHH MTV OWH Khang Vigt
Chieu dai cua hinh chfr nhat sau khi giam la: Chieu rpng ciaa hinh chiJ nhat sau khi giam la: Dien tich cua hinh chiJ nhat mdi la:
x - 2(m) | - 2 ( m ) ( x - 2 ) - - 2 U Theo dau bai, ta c6 phúdng trinh
2' 2 ( x - 2 ) ,2 2 <=> 2 x - x + 4 = — 2 4 o x ^ - 12x+ 16 = 0 fit A ' = 3 6 - 16 = 20, N/A' = 2^/5
X| = 6 + 2\/5 (thoa man dieu kien x > 4)
X2 = 6 - 2^y5 (khong thoa man dieu kien x > 4)
Vay chieu dai cua hinh chú nhat da cho la 6 + 2^5 (m)
Nhan xet: Giai bai toan bang each lap phúdng trinh, loai toan c6 noi dung
hinh hoc la dang bai toan de, quen thupc dói vdi moi hoc sinh.
CSu 4. 1) MB, MC la cac ticp tuyen
ciia dirdng Iron (O) (gt) = > M B 1 0 B , M C 1 0 C
=i> MBO = 90" , MCO = 90" . M - Do do M, B, O, C cung Ihupc difdng tr6n dudng kinh OM.
2) MB, MC la cac tiep tuyen cua dúdng tron (O) (gt)
=> OM la tia phan giac goc BOC (Tinh chát cua hai tiep tuyen c^t nhau) => MOB = - B O C . Ma B B ^ - -BOC (He qua gdc noi tiep). 2 2
; f;
Dodo MOB = BB'C
Xet ABOM va AOB'E c6: MBO = EOB' (= 90"), OB = OB' = (= R) MOB = CB'Ẹ Do do ABOM = AOB'E (g.c.g) => OM = B'Ẹ
Matkhacco MOB = OWE ^ OM//B'E
Tiif giac MOB'E cd OM // B'E, OM = B'E => Tu" giac MOB'E la hinh binh hanh=>ME = OB' =R
Luy$n giai lii frijflc ki thi vao I6p 10 ba mign BJc. Trung, Nam mOn Tôn _ Nguyjn Difc Tán
OB R 1
3) AOBM vuong tai B => sinBMO = = = - => B M O = 30" OM 2R 2 OM 2R 2
Ta CO OMC = OMB = 30", K O M = OMB (so le trong va M B // OE). Nen iCOM = 30". • . , : ^.cn^,,. . ? . ^ , .
OMC + COM = 90" (ACMO vuong tai M). Do d6 COM = 60"
AKCO vuong tai C ^ cosKOC - — ^ — = — z=>OK =
• , O K 2 OK 3
Ma O c o d i n h .
2 /3R Vay K di dong tren dúdng tron tarn O, ban kinh — - — Vay K di dong tren dúdng tron tarn O, ban kinh — - —
Nhan xet: Cac cau 1), 2) raft quen thuoc. Cau 3) khong kho khan l^m, chung ta nhan ra KOC = 30". Do vay c6 diTdc OK =
3
CSu 5. V i a, b, c > 0 thoa man a + b + c = 4. Nen 4 . a, 4 > b, 4 > c.
D o d 6 V ? + Vb^ + t / ? > V ? + ^ + V 7 = a + b + c = 4
Vay V 7 + Vb^ + V ? > 7 ^ - 2 V 2
Nhan xet: Tuf a, b, c > 0 thoa man a + b + c = 4 de c6 4 > a, 4 > b, 4 > c den vdi Idi giai tren that hay, s^ng taọ Cac ban hay tim them cac each giai khac nffa cho bai toan naỵ
V Dlfe S O 14
KY THI TUYEN SINH VAO LdP 10 THPT, TJNH DAK LAK
NAM HOC 2012 - 2013
CSu 1. (2,5 diem) • . . ...
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