Dir^ng thang A B qua A va vuong g6c C H => A B : x + 2y - 1 6 = 0. Gpi H , M Ian lúpt la chan duTcfng cao va difcfng trung tuyen k6 tilf C Khi do C H : 2 x - y + 13 = 0, C M : 6 x - 1 3 y + 29 = 0.
Ta C O C = C H n C M . Toa dp diem C la nghiem cua h$:
•C(-7; - 1 ) . 2 x - y + 13 = 0 Jx = - 7
6 x - 1 3 y + 29 = 0 \y = -\
Tifdng tif M - C M n A B . Toa dp diem M la nghipm cua h$: x + 2 y - 1 6 = 0
6 x - 1 3 y + 2 9 - 0
x = 6
M la irung diem cua AB => B(8; 4).
2. Viet phU(/n)4 trinh dudnfi tron nf-oai tiep tarn f-idc ABC.
PhiTdng trinh diTcJng tron (C) can tim c6 dang + - 2ax - 2by + c = 0 vd â + b ^ - o O .
Vi A, B, C thuoc dirdng trbn (C) nen ta c6 h? 5 2 - 8 a - 1 2 b + c = 0 8 0 - 1 6 a - 8 b + c = 0 <=> 50 + 14a + 2b + c - 0 a = 2 b = - c = -72 b = - 3 Vay (C): + y ^ - 4 x + 6 y - 7 2 = 0. Cfiu Viạ 1. Chiinfi minh...
VT = 2cosa ^cos2a sina ^ +
sin2a cosa = 2cosa
cos2ạcosa + sin2ạsina sin2ạcosa = 2cosa cos(2a-a) _ 2cosa _ 2cosa _ 1 _
sin2ạcosa sin2a 2sinạcosa sina
2. Tinh...
16 9
Ta c6:cos^a = 1 -sin^a = 1 = — =>cosa = - v i - < a < - - 25 25 Do d6: sin n — + a 2 = cosa = —• 5 4 3 24 2 • sin2a = 2sinạcosa = 2 = — ; cos2a = 1 - 2sin a = 1 - 2.
5 5 25 v 5 y
J_
"25 • tan2a si II2 a 24
cos2a 7
Cfiu Vilạ Lap phumn trinh chinh tac ciia clip (E), biet (E) c6 mot tieu diem...
x^ y2 PhiTdng trinh clip (E) c6 dang — + ^ = 1
Vielip(E)c6 tieu diem Fj(2; 0)=>c = 2=>â =b^ +4 (1). Ngoai ra: M a > b > 0 vdi < V 4 9S : ( E ) = 0 — + - ^ : = 1 ( 2 ) . â 9b2 Tilf (1) va (2) ta suy ra a^ = 9 b^^^s' 224 x^
Vay phiTcJng trinh chinh tic cua clip la (E): — + i — = l .
9 5
Cfiu VIb.
1. ChvCni* minh...
_ 1 - c o s a + cos2a 2 c o s^ a - c o s a cosa(2cosa -1)
V 1 = — = c o t a
sin2a - sina 2sinacosa - sina sină2cosa -1)
2. Tinh...
Tir tan 371 - + a = 2 => cota = -2 tana = - -
2
Ta c6:
• sin 571 • + a = cosa = —
Vl + tan^a N/5
• cos(7t + 2a) -cos2a = 1 - 2cos^a = 1-2
do — < a < T: 2 ^ 2 ^ ^ V 45 J 3 5
Cfiu Vllb. Lap phUitn^ trinh chinh tac ciia clip (E), biet (E) di qua diem.
x^ y^ Phi/cfng trinh clip (E) c6 dang — + — = 1
â b^ Tam giac MFjFj vuong tai M nen
OM = OF, =OF2 c:> ( 3 ' 2 + (4^ a > b > 0 a > b > 0 vdi - V c o c ^ = 5 < = > a ^ - b ^ = 5 ( l ) . Ngoai ra M e (E) <=> — + — = 1 (2) 53^ Sb^ Tuf (1) va (2) ta suy ra â = 9 va b^ = 4. „2 2
Vay phiTctng trinh chinh t^c cua elip la (E): — + = 1 9 4
TuyBn chqn 39 06 thJ sac hpc kl mon loan lop i u iviang cao - rngm iryiig iiiu
D E S O 14 D E THI HOC KJ II MON T O A N L d P 10 TRUdNG THPT H A I B A T R U I M G - T H C T A T H I ^ N H U i TRUdNG THPT H A I B A T R U I M G - T H C T A T H I ^ N H U i
Cfiu Ị (3,0 diem)
1. Giai ba't phiTdng trinh < 2. -7x + 10 -7x + 10 2. Giai ba't phiTdng trinh Vx^ -3x + 3 < 2x - 1 . 3. Tim m de he baft phifdng trinh 5x-x^ >0
m^x + 16>m'* -4x CO nghiem.
CSu IỊ (1,0 diem)
Thong ke diem kiem tra cua \dp IOC, giao vien bp mon thu diTpc so lieu: Diem 0 1 2 3 4 5 6 7 8 9 10 Diem 0 1 2 3 4 5 6 7 8 9 10
Tan so 1 1 1 5 6 7 11 5 4 2 2 N = 45 Tinh: So trung binh, so trung vi, phiTPng sai va dp lech chuan (chinh xdc den Tinh: So trung binh, so trung vi, phiTPng sai va dp lech chuan (chinh xdc den hang chuc).
CSu IIỊ (2,0 diem)
1. Tim m de bat phiTPng trinh (m + l)x^-2(m + l ) - l <0 nghiem diing vdi
mpi gia tri cua x thupc K.
2. Cho tanx = -2. Tinh gia tri cua bieu thtfc: A = 2sinx + 3cosx 2cosx - 5sinx
3. Rut gpn bieu thiJc: B = l-2sin^a 2cos^a-l cosa + sina cosa - sina cosa + sina cosa - sina
3
CSu IV. (2,0 diem) Trong mat phang tpa dp Oxy cho tam giac ABC vdi A(l; 2), B(2; -3),C(3; 5). B(2; -3),C(3; 5).
1. Viét phúdng trinh tong quat cua diTcJng thang AC.
2. Viet phiTdng trinh diTcJng tron tam B va tiep xuc vdi diTcfng thing AC. 3. Viet phiTPng trinh difdng thangAvuong goc vdi diTdng thing AB va tao 3. Viet phiTPng trinh difdng thangAvuong goc vdi diTdng thing AB va tao vdi hai true tpa dp mot tam giac c6 dien tich b^ng 22,5.
CSu V. (7,5 diem) Trong mat phing tpa dp Oxy cho elip(E): — + ^ = 1.
1. Xac dinh tpa dp cac tieu diem va tam sai cua elip (E).
2. Cho hai diem M, N e (E) sao cho MP, + NFj = 7. Tinh MF2 + NF,.
CSu VỊ (0,5diem) Giai he phi/Png trinh x^Cy + l)(x + y +1) = (x -l)(3x -1) xy + x + l-x^ = 0 xy + x + l-x^ = 0
H U d N G D A N - D A P S O
CSu Ị
Ị Gicii hat phmnf- trinh ... . Ml i
BPT da cho tiTPng di/Png ^ ^ ^ ' ' ^ ^ + 27 _2 < Q ^ -2x + 7 ^^
x" -7x + 10
—2x + 7
Lap bang xcl dau r(x) = ^ — — va difa vao bang xdt dau viTa lap ta tim
2:1 2
x'' -7x + 10
dirpc tap n g h i e m c u a bat phiTPng trinh da cho la S =
2. Gicii bat phU(mf> trinh ...
-3x + 3>0 2 x- l> 0 <:><; 2 x- l> 0 <:><; x^ -3x + 3<(2x- l ) ^ Ta CO Vx^ -3x + 3 < 2x -1 u[5; + 0 0 ) . X > — 2 3 x ^ - x - 2 > 0 1 X > — 2 o x > l . X < —3 hoac X >1
3. Tim m de he hat phUifnfi trinh...
Ta CO :
• m^x + 16 > m"* - 4x o (m^ + 4)x > m'* -16 o X > m^ - 4. • .^x-x-^ >0<:z>0<x<5. • .^x-x-^ >0<:z>0<x<5.
He bat phiTPng trinh da cho c6 n g h i e m o m ^ - 4 < 5 o m <3.
Cau IỊ Tinh: So trun}^ hinh, so t run if vị phumfi sai va do l^ch chudn (chinh xdc
den hanfi chuc).
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