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so crAo D TAO xi rm rUYEN sINH LoP to rHPTNAU Hec zozo - zozt
Kh6a ngiry 171712020
oAp Ax-THANG DIEMM6n thi: TOAN
0'5
1)
T{nh gid tr! cfto bi6u thrbc A khi r - 4.
Thay r - 4 (thoa mdn DKXD) vdo bitiu thric A, tinhdugc: .43
4
GI
0t
lr0
2)
r-Vr+1
1
1
2
- (c-r)(.6+r)
(c(l;
B- 3
J" -t3 + )-(
Ch*ngminh B - +Jr +t
.6+r)J-" +s
,(l; - r)
0'5
BNi I2,0 didm
3)
Tim ttit crt gid tr! crta r it| bi\u thtbc P - 2A.B + J " dqt gid tr! nhd nhdt.
P-2A.B+J;:#r+J;
Tac6: P -2 -++J; -2- +> 0 voimoi r > 0.
Jr +z Jr +2-Suy ra P > 2. Dingthric xtty rakhi vd chi khi r - 0
KL: r - 0 thi bi6u thric P dqt gi6 tri nhO nh6t.
l15
VAn t6c di xe dpp cira An la r * I (km/h).
Thdi gian An di b9 ttr nhe An dtin nhd Binh l' 3a - (gio).
... + r' +9r - 36: o <+ (r - 3)(" +12) - o <+
,Tinh vQn tbc iti b? crta An.
LAp lupn d6n d6n phucrng trinh3
Thcri gian An di xe d4p tir nha Binh v0
Gqi v0n di b0 cua An lir r (dcrn vi: km/h, u > 0).
r-3r--t2
3nhaAnh r+g Gio).
33r r*9 4
Bii II2,0 diam
I
1)
Di6mv Dfp 6nBni
kiQn lopi r 12 , thu 14i r - 3 thoa mdn y6u u bii to6n.
KL
hqrp di
t6c di ctra An la 3 km/h.0,5
2)
Tinh diQn tich bi mfit cfia qud bdng bdn.
S - 4trR2 x 4x 3,14 x22 - 50,24(.-').bc mdt cira qui b6ng ban do li:DiQn tfch
Ir0
r)
Vdi b - 1 + + - 1 + u : 2(thoam6nDKXD).y -l
v
KL: hQ phucrng trinh co nghiQm duy nh6t le (r; y): (r'r).
Gidi hQ phwong trinh
<+ .... e
2r * 3b - 5
4r - b : 3
2r* 3 :by -l
4r- 1 :3y -l
DKXD: U =L.1
DAt
- -b, tac6hq
y-IGiai he
b:lf:l
2r * 3b :54r-b:3
0,75
2a)
Ggi tgadO diem ,4 la (rr;Ao). Do cli6m ,4 thu6c tryc Oy n€n ro - 0.
Do di6m ,4 thuQc dudrng thing (d),A : n'Lr * 4 n6n
ut: ffine * 4 - m.0 * 4 - 4.
KL: tsa d0 di6m A la (0;a).
fim cua m A.
0,75b) Tim tiit cd gid tr! cfia m AO dwong thdng (d) cdt tryc Or tgi itilm B sao cho
tam gidc OAB ld tam gidc cfrn.
(*utrr). oo di6m B thuQc tryc or ndn vo - 0.
Vi di6m B thuQc ducmg theng (d),y -- rrln + 4 dan d6n 0 - mna * 4
Yt m*O + nB:a * OB -prl - l#lVi A OB - 900 n€nclOtam giitc OAB ldtam gitrccdnthi OA - OB. Md OA:4n€n OB - 4.
KL:m-l
Ggi tga <t0 cli6m B le
m-lm--l
m--L
Giai phuong trinh: l=l - 4 e.. * [- l*l t
BNi III^ . -.;./,) drcm
2b)
BNi IV
a00(rl(
1r0l) Chirng minh trb gitic BHEK ld ttb gitic nQi tiiip.
2
Di6rrD6p 6nBei Y
)
,
Chtmg minh dugc BHE - 900 vir
Suy ra BHE + BKE - 1800.
Lap luan d6n Aen fr giAc BHEK la ffi^, ,.i
grac nQl trep.
BKE : 900.
A
H
E
F
lr0
2)
Ap dgng he thftc lugng cho L,AEB vu6ng tqi E, dulng cao EH c6:
BH,BA _ BE2.
Chtmg minh tuong tg c6: BK.BC : BE2.
Y$Y BH,BA : BK,BC,
Chftng minh BH.BA: BK.BC.
lr0
3)
-
-^chtmg minh dusc BHK - BEK (l). ( BHBK le tf gitrc nQi ti6p)
Chimg minh dugc BEK : BCE (2). (Cung phU voi EBC )
Chimg minh dusc frE - ffi (3). ( BCEF la tri gitcnQi ti6p)
^ ^chimg minh dusc HFE - FHI (4). (tam giitc FHI c6n tai /. )
Ttr ( l),(2),(3), (4) suy ra ffiK -frt. Do A.ABCnhqn, hai di6m I vd Knim ctrng phia AOi vOi duong thing HF n6n I/, I, K li ba ili6m thing hing.
hdng.Ch*ng minh ba th'm H ,I,K ld ba
3,0 diam
0r5
Bni v0,5 diam
Gidiphwongtrinh J" +,h. 1- 12 *!
Lap luan dan Aen r - | (thoa mfrn DKXD).
KL: phuong trinh co nghiQm duy ntr6t lir r - 1.
-0.3r -2 -l,
+ zJr +z 3r -2 -2r2 *2
3r -2 - 12 +L
. . <+,(* -r)' * (.6- r)' * (
2DKXD: r ) -.-3
Ji+
Luu f:.c6c c6ch ldm kh6c n6u dring hqc sinh v6n tluqc di6m tuong img vdi bitiu ditim cria
ddn ch6m.uongH
J
Di6mDdp 6nBii f
K
23
a
,(
,/ov